Kuta Software - Infinite Geometry                                                                                                                                                          Name___________________________________
                         Special Right Triangles                                                                                                                                                                                                         Date________________  Period____
                         Find the missing side lengths.  Leave your answers as radicals in simplest form.
                         1)                                                                                                                                                                       2)  
                                                              b
                                                                45°                                                                                                                                                   4
                                                                                                                                                                                                                                             x
                                   2 2                                                                                                                                                                              45°
                                                                  a
                                                                                                                                                                                                                          y
                         3)                                                                                                                                                                       4)  
                                    3 2 45°                         x                                                                                                                                                    45°              x
                                                                                                                                                                                                            3 2
                                        2
                                                                y                                                                                                                                                                      y
                         5)                                                                                                                                                                       6)  
                                                                                                                                                                                                                            2 6
                                         45°              6
                                    y                                                                                                                                                                               45°
                                                                                                                                                                                                                  y                            x
                                                      x
                         7)                                                                                                                                                                       8)  
                                                  x                               y                                                                                                                                                    u
                                                                                                                                                                                                            2
                                                                         60°
                                                                                                                                                                                                                                        30°
                                                          16
                                                                                                                                                                                                                                    v
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                          9)                                                                                                                                                                        10)  
                                                        v                                                                                                                                                                             8 5
                                                                                                                                                                                                                        60°
                                                                                 8                                                                                                                                 y
                                                      u                60°                                                                                                                                                                          x
                          11)                                                                                                                                                                       12)  
                                               x                                                                                                                                                                       10                    x
                                                                  5 3
                                             60°                                                                                                                                                                        60°
                                                   y                                                                                                                                                                          y
                          13)                                                                                                                                                                       14)  
                                                                                                                                                                                                                                     y
                                              u                             v
                                                                     45°
                                                        8 2                                                                                                                                                       12
                                                                                                                                                                                                                                         x
                                                                                                                                                                                                                          30°
                          15)                                                                                                                                                                       16)  
                                                       a                                                                                                                                                                         11 3
                                                                                       b
                                                                             60°                                                                                                                                              30°
                                                                                                                                                                                                                                                                b
                                                                3                                                                                                                                                                   a
                          17)                                                                                                                                                                       18)  
                                                                                                                                                                                                                             7
                                        2 2                                                                                                                                                                                                        m
                                                                   a
                                                                                                                                                                                                                          45°
                                             60°                                                                                                                                                                                 n
                                                   b
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                          Kuta Software - Infinite Geometry                                                                                                                                                            Name___________________________________
                          Special Right Triangles                                                                                                                                                                                                           Date________________  Period____
                          Find the missing side lengths.  Leave your answers as radicals in simplest form.
                          1)                                                                                                                                                                        2)  
                                                               b
                                                                 45°                                                                                                                                                     4
                                                                                                                                                                                                                                                x
                                    2 2                                                                                                                                                                               45°
                                                                   a
                                                                                                                                                                                                                             y
                                         a = 4,  b = 2                                2                                                                                                                             x = 2                  2,  y = 2                        2
                          3)                                                                                                                                                                        4)  
                                    3 2 45°                          x                                                                                                                                                      45°              x
                                                                                                                                                                                                              3 2
                                         2
                                                                 y                                                                                                                                                                        y
                                                                           3 2                                                                                                                                      x = 6,  y = 3                                2
                                          x = 3,  y = 
                                                                                 2
                          5)                                                                                                                                                                        6)  
                                                                                                                                                                                                                               2 6
                                         45°              6
                                    y                                                                                                                                                                                 45°
                                                                                                                                                                                                                     y                             x
                                                       x
                                                                                                                                                                                                                    x = 2                  3,  y = 2                        3
                                          x = 3                 2,  y = 3                         2
                          7)                                                                                                                                                                        8)  
                                                   x                               y                                                                                                                                                      u
                                                                                                                                                                                                              2
                                                                         60°
                                                                                                                                                                                                                                           30°
                                                          16
                                                                                                                                                                                                                                       v
                                          x = 8                 3,  y = 8                                                                                                                                           u = 4,  v = 2                               3
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                         9)                                                                                                                                                                        10)  
                                                        v                                                                                                                                                                           8 5
                                                                                                                                                                                                                      60°
                                                                                 8                                                                                                                                y
                                                     u                60°                                                                                                                                                                         x
                                         u = 16,  v = 8                                  3                                                                                                                         x = 4                 15,  y = 4                           5
                         11)                                                                                                                                                                       12)  
                                               x                                                                                                                                                                     10                     x
                                                                  5 3
                                             60°                                                                                                                                                                      60°
                                                   y                                                                                                                                                                        y
                                         x = 10,  y = 5                                                                                                                                                            x = 5                 3,  y = 5
                         13)                                                                                                                                                                       14)  
                                                                                                                                                                                                                                   y
                                             u                             v
                                                                    45°
                                                        8 2                                                                                                                                                     12
                                                                                                                                                                                                                                       x
                                                                                                                                                                                                                        30°
                                         u = 8,  v = 8
                                                                                                                                                                                                                   x = 8                 3,  y = 4                        3
                         15)                                                                                                                                                                       16)  
                                                      a                                                                                                                                                                        11 3
                                                                                      b
                                                                             60°                                                                                                                                             30°
                                                                                                                                                                                                                                                              b
                                                               3                                                                                                                                                                  a
                                                     3 3                               3                                                                                                                          a = 22,  b = 11
                                         a =                         ,  b = 
                                                           2                           2
                         17)                                                                                                                                                                       18)  
                                                                                                                                                                                                                           7
                                       2 2                                                                                                                                                                                                        m
                                                                  a
                                                                                                                                                                                                                        45°
                                             60°                                                                                                                                                                               n
                                                   b                                                                                                                                                                            7 2                               7 2
                                                                                                                                                                                                                  m =                           ,  n = 
                                         a =                6,  b =                      2                                                                                                                                            2                                2
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                                                                                                                                                                             Infinite Geometry
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