Question

question 6 (5 points) listen determine the value of x. a) 44.78 b) 0.02 c) 3.22 d) 70.57

Explanation:

Step1: Identify trigonometric relation

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 15^{\circ}$, the opposite side to the angle $\theta$ is $12$ and the adjacent side is $x$. So, $\tan15^{\circ}=\frac{12}{x}$.

Step2: Recall the value of $\tan15^{\circ}$

We know that $\tan15^{\circ}=2 - \sqrt{3}\approx2 - 1.732 = 0.268$.

Step3: Solve for $x$

From $\tan15^{\circ}=\frac{12}{x}$, we can rewrite it as $x=\frac{12}{\tan15^{\circ}}$. Substituting $\tan15^{\circ}\approx0.268$, we get $x=\frac{12}{0.268}\approx44.78$.

Answer:

A. 44.78