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.) 23 54° 90° 36° x sin 36° ≈ 0.588 cos 36° ≈ 0.809 tan 36° ≈ 0.727 a. 16.72 b. 18.61 c. 39.12 d. 13.52 e. 31.64 f. 28.43

Explanation:

Step1: Identify trigonometric ratio

For the $36^\circ$ angle, the side of length 23 is the opposite side, and $x$ is the adjacent side. Use tangent ratio: $\tan\theta = \frac{\text{opposite}}{\text{adjacent}}$

Step2: Rearrange to solve for $x$

$x = \frac{\text{opposite}}{\tan 36^\circ}$

Step3: Substitute values and calculate

Substitute opposite = 23, $\tan 36^\circ \approx 0.727$:
$x = \frac{23}{0.727} \approx 31.64$

Answer:

E. 31.64