In a right-angled triangle ABC AB = 15 and one of the legs is 9. Find the tangent of the angle CAB

In a right-angled triangle ABC AB = 15 and one of the legs is 9. Find the tangent of the angle CAB of the smaller of the acute angles

The CAB is a smaller angle, hence the BC is the smaller side.

If BC = 9, AB = 15, then:

1) AC ^ 2 = AB ^ 2 – BC ^ 2 = 225 – 81 = 144.

AC = 12

AC from under the root is 12.

2) Find the tangent of the angle CAB.

tg angle CAB = CB / AC = 9/12 = 3/4 = 0.75

Answer: tg angle CAB = 0.75 or 3/4.