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

Option A. 30°

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 =(AB)/(BC)`

Where ∠ C = ∅ (theta)

`tan\theta =(6)/(6√(3))=(1)/(√(3))`

`\theta =tan^(-1)((1)/(√(3)))=30`

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

Answer 2

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

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