Chapter 11.2, Problem 47SPR

To determine

To find:

The value of $x$ and $y$ .

Answer to Problem 47SPR

The value of $x=9$ and $y=15.59$ .

Explanation of Solution

Given information:

  

Calculation:

Apply the sine law to find the value of $x$ .

  $\sin \theta =\frac{p}{h}$

Substitute $\theta ={30}^{\circ }$ , $p=x$ and $h=18$ .

  $\begin{array}{c}\sin {30}^{\circ }=\frac{x}{18}\\ \frac{1}{2}=\frac{x}{18}\\ x=\frac{18}{2}\\ =9\end{array}$

Now, apply the Pythagorean theorem to find the value of $y$ .

  $\begin{array}{c}{x}^2+y^2={18}^2\\ y^2={18}^2-x^2\\ y^2=324-9^2\\ y^2=324-81\\ y^2=243\\ y=\sqrt{243}\\ =15.59\end{array}$

Hence, the value of $x=9$ and $y=15.59$ .