8.4. 45-45-90 Right Triangles http://www.ck12.org
Use thex:x:x
√
2 ratio.T V=6 because it is equal toST. So,SV= 6
√
2.
Example B
Find the length ofx.
Again, use thex:x:x
√
2 ratio. We are given the hypotenuse, so we need to solve forxin the ratio.x√
2 = 16
x=16
√
2
·
√
2
√
2
x==16
√
2
2
x= 8√
2
Note that werationalized the denominator. Whenever there is a radical in the denominator of a fraction, multiply
the top and bottom by that radical. This will cancel out the radical from the denominator and reduce the fraction.
Example C
A square has a diagonal with length 10, what are the lengths of the sides?
Draw a picture.