Question

If 3tan² A − 1 = 0 and angle A is acute, the measure of angle A is ______.

Options

• 20°

• 45°

• 60°

• 30°

Answer 1

If 3tan² A − 1 = 0 and angle A is acute, the measure of angle A is 30°.

Explanation:

Given 3tan² A − 1 = 0

3tan² A = 1

\[\tan^2 A = \frac{1}{3}\]

\[\tan A = \frac{1}{\sqrt{3}}\] (taking the positive value for an acute angle).

Since \[\tan 30^\circ = \frac{1}{\sqrt{3}}\], the measure of angle A is 30°.