Chapter 9, Problem 22CT

To determine

Tofind:The value of $c$

Answer to Problem 22CT

  $c\approx 19$

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-

  $\begin{array}{l}\cos A=\frac{Adjacent}{Hypotenuse}\\ \Rightarrow \cos {65}^{\circ }=\frac{AC}{AB}\\ \Rightarrow 0.4226=\frac{8}{c}\\ \Rightarrow c=\frac{8}{0.4226}\\ \Rightarrow c=18.93\\ \Rightarrow c\approx 19\end{array}$