Please help me solve this question. The figure shows a triangle ABC where ˂ABC = 35°. H lies on BC such that the length of HC is twice that of BH. Find <ACB.

Question

Please help me solve this question.

The figure shows a triangle ABC where ˂ABC = 35°. H lies on BC such that the length of HC is twice that of BH. Find <ACB.

Answer 1

I let ∠A = 90°, so ∠C = 55º This seems too easy, but it works.

Since BC = 3x, AC/3x = Sin(35º) and AC = 1.72x. Then AB/3x = Cos(35º) and AB = 2.46x

Using the Pythagorean Theorem, √[(2.46x)² + (1.72x)² ] = 3x which is BC.