9.4

Question 1

Theorem 9.8

Answer 1

In a 45 degree - 45 degree - 90 degree triangle, the hypotenuse is root 2 times as long as each leg. That is, the side-length ratios of leg-leg-hyp are x:x:x root 2

***hyp = leg * root 2

Question 2

Theorem 9.9

Answer 2

In a 30 degree - 60 degree - 90 degree triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is root 3 times as long as the shorter leg. That is, the side-length ratios of short leg:long leg:hyp are x:x root 3:2x

***hyp = 2 * short
long = short * root 3