Chapter 9, Problem 33CR

To determine

Tofind:The value of $b$

Answer to Problem 33CR

  $b\approx 11$

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-

  $\begin{array}{l}\cos A=\frac{Adjacent}{Hypotenuse}\\ \Rightarrow \cos {40}^{\circ }=\frac{AC}{AB}\\ \Rightarrow 0.7660=\frac{b}{15}\\ \Rightarrow b=15\left(0.7660\right)\\ \Rightarrow b=11.4906\\ \Rightarrow b\approx 11\end{array}$