Question

question 1 of 40 in the triangle below, what is the length of the side opposite the 60° angle? a. 3√2 b. √3 c. 3√3 d. 6

Explanation:

Step1: Recall trigonometric ratio

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

Step2: Use tangent formula

We know that $\tan60^{\circ}=\sqrt{3}$, and $\tan60^{\circ}=\frac{\text{opposite side to }60^{\circ}}{3}$.

Step3: Solve for opposite side

Let the opposite side to the $60^{\circ}$ angle be $x$. Then $\sqrt{3}=\frac{x}{3}$, so $x = 3\sqrt{3}$.

Answer:

C. $3\sqrt{3}$