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. 13.52 b. 28.43 c. 31.64 d. 16.72

Explanation:

Step1: Identify trigonometric ratio

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. In the right - triangle, for the $36^{\circ}$ angle, the opposite side 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:

C. 31.64