A survey team is...

Question

A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 25∘. From a point 1000 feet closer to the mountain along the plain, they find that the angle of elevation is 29∘.

How high (in feet) is the mountain?

Answer 1

Draw a figure.

h is the ht of the mountain; x is the distance from the nearer observation point to the mountain.

h/x=tan 29 and h/(x+1000)=tan 25.

Eliminate the h and solve for x; then get h.