Chapter 9.8, Problem 16E

To determine

Tofind:The value of $x$

Answer to Problem 16E

  $x\approx 4$

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-

  $\begin{array}{l}\sin {40}^{\circ }=\frac{Opposite}{Hypotenuse}\\ \Rightarrow 0.6427=\frac{x}{6}\\ \Rightarrow x=\left(0.6427\right)6\\ \Rightarrow x=3.8567\\ \Rightarrow x\approx 4\end{array}$