Question

question 5 (5 points) determine the value of x. a) 0.22 b) 55.8 c) 4.625 d) 4.59

Explanation:

Step1: Identify the trigonometric relation

In a right - triangle, we use the tangent function. $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 74^{\circ}$, the opposite side to the angle $74^{\circ}$ is $16$ and the adjacent side is $x$. So, $\tan(74^{\circ})=\frac{16}{x}$.

Step2: Solve for $x$

We know that $\tan(74^{\circ})\approx3.4874$. Then, $x = \frac{16}{\tan(74^{\circ})}$. Substituting the value of $\tan(74^{\circ})$, we get $x=\frac{16}{3.4874}\approx4.59$.

Answer:

D. 4.59