Chapter 9.8, Problem 17E

To determine

Tofind:The value of $x$

Answer to Problem 17E

  $x\approx 12$

Explanation of Solution

Given information:

Concept Used:

In a right-angled triangle ABC, sine for acute angle $\angle A$ is the ratio of length of side opposite to angle $\angle A$ to the length of hypotenuse and cosine of acute angle $\angle A$ is the ratio of length of side adjacent to angle $\angle A$ to the length of hypotenuse.

Calculation:

Basis definition we can say-

  $\begin{array}{l}\cos {36}^{\circ }=\frac{Adjacent}{Hypotenuse}\\ \Rightarrow 0.8090=\frac{x}{15}\\ \Rightarrow x=\left(0.8090\right)15\\ \Rightarrow x=12.1352\\ \Rightarrow x\approx 12\end{array}$