Question

In traveling across flat land, you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5°. After you drive x = 9 miles closer to the mountain, the angle of elevation is 9°. Approximate the height of the mountain. (Round your answer to one decimal place.)
the picture in the link below:
www.webassign.net/larprecalcaga5/5-2-080.gif

Answer 1

You can find all the angles of the obtuse triangle, and you have one side.
So, find the side which is also the hypotenuse of the other triangle using the sine law.
Now in the right-angled triangle, use sin 9 = height/hypotenuse to find the height

Answer 2

Tan3.5 = h/d, h = d*Tan3.5.
Tan9 = h/(d-9), h = (d-9)*Tan9.

h = d*Tan3.5 = (d-9)*Tan9.
d*Tan3.5 = (d-9)*Tan9, Divide both sides by Tan3.5:
d = (d-9)*2.59,
d = 2.59d - 23.3,
-1.59d = -23.3,
d = 14.7 miles.

h = d*Tan3.5 = 14.7*Tan3.5 = 0.90 miles.