Question

what is the approximate value of x in the diagram below? (hint: you will need to use one of the trigonometric ratios given in the table.) sin 36° ≈ 0.588 cos 36° ≈ 0.809 tan 36° ≈ 0.727 a. 39.12 b. 18.61 c. 13.52 d. 31.64 e. 28.43 f. 16.72

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, we know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 36^{\circ}$, the opposite side to the $36^{\circ}$ angle is 23 and the adjacent side is $x$. So, $\tan36^{\circ}=\frac{23}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{23}{\tan36^{\circ}}$. Given that $\tan36^{\circ}\approx0.727$, then $x=\frac{23}{0.727}\approx31.64$.

Answer:

D. 31.64