Chapter 8.6, Problem 4WE

To determine

To find the values of $x$ and $y$ by using the triangle shown below.

  

Answer to Problem 4WE

  $x=54\&y=64$ .

Explanation of Solution

Given:

  

Calculation:

In the given triangle,

  $\begin{array}{l}\sin {40}^{\circ }=\frac{x}{84}\\ \Rightarrow x=84\cdot \sin {40}^{\circ }\\ \Rightarrow x=53.9941\\ \Rightarrow x\approx 54\end{array}$

&

  $\begin{array}{l}\cos {40}^{\circ }=\frac{y}{84}\\ \Rightarrow y=84\cdot \cos {40}^{\circ }\\ \Rightarrow y=64.3477\\ \Rightarrow y\approx 64\end{array}$