Chapter 8.5, Problem 15WE

To determine

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

Answer to Problem 15WE

$w=75$ and $z\approx 89$

Explanation of Solution

Given information:

Right angle triangles

It can be observed the triangle contains ${30}^{\circ }$ at one of it vertex with hypotenuse $=150$ and perpendicular $=w$

Then from sine rule, we have $\sin {30}^{\circ }=\frac{\text{perpendicular}}{\text{hypotenuse}}$

$\begin{array}{l}\Rightarrow \frac{1}{2}=\frac{w}{150}\\ \Rightarrow w=\frac{150}{2}\\ \therefore w=75\end{array}$

The other triangle contains ${40}^{\circ }$ at one of its vertex with perpendicular $=75$ and base

$=z$ then

From tan rule, we have $\tan {40}^{\circ }=\frac{\text{perpendicular}}{\text{base}}$

  $\begin{array}{l}\Rightarrow 0.839=\frac{\text{perpendicular}}{\text{base}}\\ \Rightarrow z=\frac{75}{0.839}\\ \Rightarrow z=89.38\\ \therefore z\approx 89\end{array}$

Hence, $w=75$ and

$z\approx 89$