Question

one leg of a right triangle measures 6 inches. the remaining leg measures 6\sqrt{3} inches. what is the measure of the angle opposite the leg that is 6 inches long? 30° 45° 60° 90°

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Let \(\theta\) be the angle opposite the leg of length \(6\) inches. The adjacent leg to \(\theta\) is \(6\sqrt{3}\) inches. So, \(\tan\theta=\frac{6}{6\sqrt{3}}\).

Step2: Simplify the expression

Simplify \(\frac{6}{6\sqrt{3}}\) by canceling out the common factor of \(6\). We get \(\frac{1}{\sqrt{3}}\). Rationalizing the denominator (multiply numerator and denominator by \(\sqrt{3}\)), we have \(\frac{\sqrt{3}}{3}\).

Step3: Recall the value of the tangent function

We know that \(\tan30^{\circ}=\frac{\sqrt{3}}{3}\).

Answer:

\(30^{\circ}\) (Option A)