Exercise 29 Page 585

Notice that the legs of the given right triangle are congruent. Therefore, we have an isosceles triangle and the acute angles are also congruent. By the Triangle Angle Sum Theorem, they must both measure 45^(∘).

In a 45^(∘)-45^(∘)-90^(∘) triangle, the legs are congruent and the hypotenuse is sqrt(2) times the length of a leg. With this information, we can find the value of each variable. 20 =x sqrt(2) Let's isolate x in above expression.

20 = x sqrt(2)

MultEqn

LHS * sqrt(2)=RHS* sqrt(2)

20sqrt(2) = x (sqrt(2))^2

PowSqrt

( sqrt(a) )^2 = a

20sqrt(2) = 2x

DivEqn

.LHS /2.=.RHS /2.

10sqrt(2) = x

RearrangeEqn

Rearrange equation

x = 10sqrt(2)

UseCalc

Use a calculator

x ≈ 14.142135...

Finaly, we will round the result to the nearest hundredth. x ≈ 14.14