If 3tan² A - 1 = 0 and angle A is acute, the measure of angle A is :

1. 20°

2. 45°

3. 60°

4. 30°

3tan² A - 1 = 0

⇒ 3tan² A = 1

⇒ tan² A = $\dfrac{1}{3}$

⇒ tan A = $\sqrt{\dfrac{1}{3}}$

⇒ tan A = $\dfrac{1}{\sqrt3}$

⇒ tan A = tan 30°

⇒ A = 30°

Hence, option 4 is the correct option.