Question

If tan A = 3 cot A, then the measure of the angle A is :

• A. 15°
• B. 30°
• C. 45°
• D. 60°

Answer 1

The Correct Option is D

Step 1: Identify the objective:
The problem requires determining the value of angle \( A \) given the equation \( \tan A = 3 \cot A \).

Step 2: Simplify the equation:
Utilize the trigonometric identity \( \cot A = \frac{1}{\tan A} \). Substituting this into the given equation yields:
\[\tan A = 3 \times \frac{1}{\tan A}\]Multiplying both sides by \( \tan A \) (assuming \( \tan A eq 0 \)) results in:
\[\tan^2 A = 3\]

Step 3: Solve for \( \tan A \):
Taking the square root of both sides gives:
\[\tan A = \sqrt{3} \quad \text{or} \quad \tan A = -\sqrt{3}\]Considering that \( \tan A = \sqrt{3} \) corresponds to \( A = 60^\circ \), and assuming \( A \) lies within the principal range of \( 0^\circ \) to \( 180^\circ \), we select \( A = 60^\circ \).

Step 4: State the final answer:
The calculated measure of angle \( A \) is \( \boxed{60^\circ} \).