Question

A certain rock rises almost straight upward from the valley floor. From one​ point, the angle of elevation of the top of the rock is 19.4degrees. From a point 117 m closer to the​ rock, the angle of elevation of the top of the rock is 37.9degrees. How high is the​ rock?

Answer 1

75.25 m to the nearest hundredth.

Explanation:

We have 2 right angled triangles here one 'inside ' the other.

Let the height of the rock be x m and the distance of the rock from the first point be y m . Then the distance of the second point from the rock = (y - 117) m.

Using trigonometry of the 2 triangles:

tan 19.4 = x/y

tan 37.9 = x / ( y - 117)

0.3522 = x/y - A.

0.7785 = x / ( y - 117) - B.

From A: x = 0.3522y

Substitute for x in B:

0.7785 = 0.3522y / (y - 117)

0.3522y = 0.7785y - 91.085

0.7785y - 0.3522y = 91.085

y = 91.085 / ( 0.7785-0.3522)

= 213.64 m

So the height x of the rock = 0.3522*213.664

= 75.25 m.