Question

PLEASE ANSWER I REALLY NEED HELP ON THIS QUESTION!

In triangle ABC, angle A = 30 degrees and angle B = 60 degrees. Point X is on side AC such that line segment BX bisects angle ABC. If AB = 12, then find the area of triangle BXA.

Answer 1

The area of triangle BXA is 15*sqrt(2).

Answer 2

12sqrt(3)

Explanation:

The diagram is below.

Since triangle ABC is a 30-60-90 triangle, we have BC = AB/2 = 6, and AC = BCsqrt(3) = 6sqrt(3).

Since angle ABC equals 60 degrees and BX bisects angle ABC, we have angle CBX equal 30 degrees, so BXC is a 30-60-90 triangle.

Since CX is opposit the 30 degree angle in triangle BXC, we have:

CX = BC / sqrt(3) = 6 / sqrt(3) = 2 sqrt(3).

Therefore, AX = AC - CX = 4 sqrt(3).