Chapter 8.5, Problem 18WE

To determine

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

Answer to Problem 18WE

$w=520$ and $z\approx 480$

Explanation of Solution

Given information:

Right angle triangles

It can be observed the triangle contains ${60}^{\circ }$ at one of it vertex with base $=w$ and perpendicular $=900$

Then from tan rule, we have $\tan {60}^{\circ }=\frac{\text{perpendicular}}{\text{base}}$

  $\begin{array}{l}\Rightarrow \sqrt{3}=\frac{900}{w}\\ \Rightarrow w=\frac{900}{\sqrt{3}}\\ \Rightarrow w=\frac{900}{\left(1.732\right)}\\ \Rightarrow w=519.615\\ \therefore w\approx 520\end{array}$

The other triangle contains

${42}^{\circ }$ at one of its vertex with same perpendicular $=900$ and base $=w+z,\text{where}w=519.615$

then from tan rule, we have

$\tan {42}^{\circ }=\frac{\text{perpendicular}}{\text{base}}$

  $\begin{array}{l}\Rightarrow 0.9004=\frac{900}{w+z}\\ \Rightarrow w+z=\frac{900}{0.9004}\\ \Rightarrow z=999.556-w\\ \Rightarrow z=999.556-519.615,\text{since}w=519.615\\ \Rightarrow z=479.941\\ \therefore z\approx 480\end{array}$

Hence, $w=520$ and $z\approx 480$