Question

triangle ABC is isosceles triangle with AB=AC and Angle A=120°. The internal angle bisector BD has length 40 root 2 units. Find the length of BC
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Answer 1

Let the angle bisector be AD

if angle A is 120°,

Angle BAD = A/2 = 60°

So,

For an isosceles triangle, angle bisector is the altitude

Hence

If altitude is P, and half base BD is B,

P/B = tan 60°

B= P/tan60°

B= 40√2/√3

B=40√(2/3)

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