Geometry 9.4 Special Right Triangles:
I) 45°: 45°:90° Triangle Theorem: in a 45°, 45°, 90° triangle,
the hypotenuse is √2 times as long as each leg.
1x: 1x: x√2
Example: if the leg of a 45°: 45°: 90° triangle is 5, what is the other leg length and the hypotenuse length?
Since the legs are equal in length, the other leg is 5.
the hypotenuse would be 5√2
II) 30 :60 : 90 triangle theorem: in a 30º , 60º , 90º triangle,
the hypotenuse is 2 times as long as the shorter leg, and the longer leg is
√3 times as long as the shorter leg.
1x : x√3 : 2x
Example: if the shorter leg of a 30º , 60º , 90º triangle is 7, what is the length of the longer leg and the hypotenuse?
the longer leg is 7√3 and the hypotenuse is (2)(7) = 14