Chapter 9.7, Problem 18E

To determine

Tofind:The value of $x$

Answer to Problem 18E

  $x=30.7176$

Explanation of Solution

Given information:

Concept Used:

In a right-angled triangle ABC, tangent for acute angle $\angle A$ is the ratio of length of side opposite to angle $\angle A$ to the length of side adjacent to $\angle A$

Calculation:

Basis definition we can say-

  $\begin{array}{l}\tan A=\frac{opposite}{adjacent}\\ \Rightarrow \tan {52}^{\circ }=\frac{x}{24}\\ \Rightarrow 1.2799=\frac{x}{24}\\ \Rightarrow x=\left(1.2799\right)24\\ \Rightarrow x=30.7176\end{array}$