Chapter 8.5, Problem 16WE

To determine

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

Answer to Problem 16WE

$w=82$ and $z\approx 154$

Explanation of Solution

Given information:

Right angle triangles

It can be observed the triangle contains ${45}^{\circ }$ at one of it vertex with base $=82$ and perpendicular $=w$

Then from tan rule, we have $\tan {45}^{\circ }=\frac{\text{perpendicular}}{\text{base}}$

$\begin{array}{l}\Rightarrow 1=\frac{w}{82}\\ \therefore w=82\end{array}$

The other triangle contains ${28}^{\circ }$ at one of its vertex with perpendicular $=w=82$ and base

$=z$ then from tan rule, we have $\tan {28}^{\circ }=\frac{\text{perpendicular}}{\text{base}}$

  $\begin{array}{l}\Rightarrow 0.5317=\frac{82}{z}\\ \Rightarrow z=\frac{82}{0.5317}\\ \Rightarrow z=154.22\\ \therefore z\approx 154\end{array}$

Hence,

$w=82$ and $z\approx 154$