Question

N triangle ABC (see sketch), AD is the angle bisector of the angle A and BH is the height from side AC. The obtuse angle between BH and AD is four times the side of DAB. How big is the angle CAB?

A. 30 B.45 C.60 D.75 E.90

Answer 1

Answer: C

Explanation:

We know that
`\angle AHB=90^(\circ)`, and thus by the exterior angle theorem,

`90^(\circ)+\alpha=4\alpha\\\\90=3\alpha\\\\\alpha=30^(\circ)`

Thus,
`\angle CAB=2\theta=\boxed{60^(\circ)}`