Find the height of the mountain.

Question

From one point on the ground, the angle of elevation of the peak of a mountain is 11°, and from a point 1 000 m closer, the angle of elevation is 15. Both points are due east of the mountain. Find the height of the mountain.

Answer 1

The gentleman above has given you all the information you need.

Now you have two equations that equal h.

So you can rewrite the equations as:

(x-1000)tan15 = xtan11

xtan15 - 1000tan15 = xtan11

x (tan15-tan11) = 1000

x = 1000 / (tan 15-tan 11)

Solve for x, then solve for h.

Good luck!

Answer 2

Let h = height of the mountain and x = distance from the base of the mountain to the first reference point.

tan11 = h/x So, h = xtan11

tan 15 = h/(x-1000). So, h = (x-1000)tan15

Therefore, xtan11 = (x-1000)tan15

Solve for x, then find h.