# angles

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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 -

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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