Question

One leg of a right triangle measures 6 inches. The remaining leg measures 6 square root of 3 inches. What is the measure of the angle opposite the leg that is 6 inches long?
30°
45°
60°
90°

Answer 1

tan(α) = opposite/adjacent = 6/(6√3) = (√3)/3

Using inverse functions, you can find the angle.
  α = arctan((√3)/3) = 30°

Answer 2

Answer:

Option A. 30°

Step-by-step explanation:

In the given triangle ABC, side AB = 6 in, side BC = 6√3 in.

We have to find the measure of angle C.

Since we know $tan\theta =\frac{AB}{BC}$

Where ∠ C = ∅ (theta)

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

$\theta =tan^{-1}(\frac{1}{\sqrt{3}})=30$

Therefore angle C is 30° is the answer. Option A is the correct option.