Chapter 11.2, Problem 46SPR

To determine

To find:

The value of $x$ and $y$ .

Answer to Problem 46SPR

The value of $x=17.9$ and $y=16$ .

Explanation of Solution

Given information:

  

Calculation:

Apply the cosine law to find the value of $y$ .

  $\cos \theta =\frac{b}{h}$

Substitute $\theta ={60}^{\circ }$ , $b=8$ and $h=y$ .

  $\begin{array}{c}\cos 60=\frac{8}{y}\\ \frac{1}{2}=\frac{8}{y}\\ y=8\cdot 2\\ =16\end{array}$

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

  $\begin{array}{c}{x}^2=8^2+{16}^2\\ x^2=64+256\\ x^2=320\\ x=\sqrt{320}\\ =17.9\end{array}$

Hence, the value of $x=17.9$ and $y=16$ .