Question

clue # 5
what is the value of x to the nearest tenth?
22
a 5.7
c 30.3
b 21.2
d 82.1

Explanation:

Step1: Identify trigonometric ratio

We use tangent: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$
Here, $\theta=75^\circ$, opposite side $=x$, adjacent side $=22$.

Step2: Rearrange to solve for x

$x = 22 \times \tan(75^\circ)$

Step3: Calculate $\tan(75^\circ)$ and x

$\tan(75^\circ) \approx 3.732$, so $x \approx 22 \times 3.732 = 82.104$

Step4: Round to nearest tenth

$x \approx 82.1$

Answer:

D. 82.1