Question

Let A,B,C be the angles of a plain triangle. If tan(A)/(2)=(1)/(3) and tan(B)/(2)=(2)/(3), then tan(C)/(2) is equal to:

• A. \( \dfrac{7}{9} \)
• B. \( \dfrac{2}{9} \)
• C. \( \dfrac{1}{3} \)
• D. (2)/(3)

Hint:

Use the half-angle tangent identity for triangle angle problems.

Answer 1

The Correct Option is A

Step 1: In a triangle, tan(A)/(2)tan(B)/(2)+tan(B)/(2)tan(C)/(2)+tan(C)/(2)tan(A)/(2)=1.
Step 2: Substitute values: (1)/(3)·(2)/(3)+(2)/(3)x+(1)/(3)x=1.
Step 3: Solve to get x=(7)/(9).