Posted by **tyler** on Sunday, March 10, 2013 at 5:15pm.

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 degrees. From a point 1225 feet closer to the mountain along the plain, they find that the angle of elevation is 30 degrees.

How high (in feet) is the mountain?

- angles -
**Reiny**, Sunday, March 10, 2013 at 5:35pm
make a sketch

let the top of mountain be T

base of mountain R

so we want TR

Let A be the point farthest from the top, let B be the closer point,

AB = 1225

In triangle TAB

angle A = 25°

angle TBR = 30° , so angle TBA =150°

leaving us with angle ATB = 5°

by the sine law:

BT/sin25 = 1225/sin 5°

BT = 1225sin25/sin5 = 5940.059

so now in the right-angled triangle TBR

sin 30 = TR/5940.059

TR = 5940.059*sin30 = 2970.03 ft

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