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 rightangled triangle TBR
sin 30 = TR/5940.059
TR = 5940.059*sin30 = 2970.03 ft