Right Triangle Trigonometry

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 32∘. From a point 3500 feet closer to the mountain along the plain, they find that the angle of elevation is 37∘

How high (in feet) is the mountain?

The mountain is  ______ feet high

Answer 1

at 32 degrees they view the mountain top

then move 3500 feet closer and view the top from 37 degrees

how high is the mountain top

construct 2 right triangles

tangents of the angles = height divided by the bases

bases = 3500+x and x

height = h

tan 32 = h/(x+3500) = about .6249

tan 37 = h/x = about .7536

h= .6249x + 3500(.6249) = .7536x

(.7536-.6249)x = 3500(.6249)

.1287x = 2871.5

x = 2871.5/.1287 = about 2231.2

h= .7536(2231.2) = 1,681.4 feet high mountain top

or since 3500 is seemingly rounded off to 2 significant digits

go with 1700 feet high= 1681 rounded off to 2 significant digits