Chapter 8.5, Problem 13WE

To determine

To find the values of $w$ and $z$

Answer to Problem 13WE

$w=60$ and $z\approx 54$

Explanation of Solution

Given information:

Right angle triangles

It can be observed that two triangles are congruent by the postulate SAS.

$$

$\Rightarrow$ The corresponding lengths are equal.

$\begin{array}{l}w=\frac{120}{2}\\ \therefore w=60\end{array}$

Thus, base $=60$ , perpendicular $=z$

$\begin{array}{l}\Rightarrow \tan 42=\frac{\text{perpendicular}}{\text{adjacent}\text{side}}\\ \Rightarrow \tan 42=\frac{z}{60}\\ \Rightarrow z=\left(60\right)\tan 42\\ \Rightarrow z=\left(60\right)\left(0.900\right)\\ \therefore z=54.024\end{array}$

Hence, $w=60$ and $z\approx 54$