Chapter 9, Problem 21CT

To determine

Tofind:The value of $a$

Answer to Problem 21CT

  $a\approx 17$

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-

  $\begin{array}{l}\tan A=\frac{opposite}{adjacent}\\ \Rightarrow \tan {65}^{\circ }=\frac{BC}{AC}\\ \Rightarrow 2.1445=\frac{a}{8}\\ \Rightarrow a=8\left(2.1445\right)\\ \Rightarrow a=17.1560\\ \Rightarrow a\approx 17\end{array}$