Question

one leg of a right - triangle measures 6 inches. the remaining leg measures 6√3 inches. what is the measure of the angle opposite the leg that is 6 inches long? 60° 45° 60° 30°

Explanation:

Step1: Recall tangent formula

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Let the angle opposite the side of length 6 inches be $\theta$, the opposite side $a = 6$ inches and the adjacent side $b=6\sqrt{3}$ inches.

Step2: Calculate the tangent value

$\tan\theta=\frac{6}{6\sqrt{3}}=\frac{1}{\sqrt{3}}$.

Step3: Find the angle

We know that if $\tan\theta=\frac{1}{\sqrt{3}}$, then $\theta = 30^{\circ}$ since $\tan30^{\circ}=\frac{1}{\sqrt{3}}$.

Answer:

$30^{\circ}$