Question

find the value of x.
question 6 (multiple choice)

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, we know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 60^{\circ}$, the opposite side to the $60^{\circ}$ angle is $x$ and the adjacent side is $5\sqrt{3}$.

Step2: Apply the tangent formula

We know that $\tan60^{\circ}=\sqrt{3}$, and $\tan60^{\circ}=\frac{x}{5\sqrt{3}}$. So, $\sqrt{3}=\frac{x}{5\sqrt{3}}$.

Step3: Solve for x

Cross - multiply: $x = \sqrt{3}\times5\sqrt{3}$. Then $x=5\times3 = 15$.

Answer:

15