one leg of a right triangle measures 6 inches. the remaining leg measures 6\\sqrt{3} inches. what is the…

Explanation:

Step1: Recall tangent formula

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

Step2: Simplify the tangent value

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

Step3: Find the angle

We know that if $\tan\theta=\frac{1}{\sqrt{3}}$, and $\theta$ is an acute angle in a right - triangle, then $\theta = 30^{\circ}$ since $\tan30^{\circ}=\frac{1}{\sqrt{3}}$.

Answer:

A. $30^{\circ}$