Question

select the correct answer. what is the value of x in the triangle? triangle image with 15, 30°, right angle, x, 60° a. 15√3 b. 7.5 c. 5 d. 5√3 e. 15

Explanation:

Step1: Identify trigonometric ratio

We use the tangent function for the 30° angle: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta=30^\circ$, opposite side is $x$, adjacent side is 15.
$\tan(30^\circ) = \frac{x}{15}$

Step2: Substitute $\tan(30^\circ)$ value

We know $\tan(30^\circ) = \frac{1}{\sqrt{3}}$. Substitute this into the equation:
$\frac{1}{\sqrt{3}} = \frac{x}{15}$

Step3: Solve for $x$

Rearrange to isolate $x$:
$x = \frac{15}{\sqrt{3}}$
Rationalize the denominator:
$x = \frac{15\sqrt{3}}{3} = 5\sqrt{3}$

Answer:

D. $5\sqrt{3}$