Question

In the triangle shown, AC = BC and ACB=120°. If AC = 8, what is the area of the triangle ABC?​

Answer 1

Answer:

CD divides triangle ABC into 2 triangles: ACD and BCD:

Δ ABC = Δ ACD + Δ BCD

[a * b * sin(120°)]/2 = [b * CD * sin(60°)]/2 + [a * CD * sin(60°)]/2

√3/4 * a * b = √3/4 * b * CD + √3/4 * a * CD

ab = CD(a + b)

CD = ab/(a + b)