math xl question from trig

Question

to measure a stone face carved on the side of the mountain, two sightings 800 feet from the base of the mountain are taken. if the angle of elevation to the bottom of the face is 27 degrees and the angle of elevation to the top is 31 degrees, what is the height of the stone face?

Answer 1

Imagine two right triangles.  Both have a base of 800.  One has an angle of 27^o and the other has an angle of 31^o.

 

We want to find the height of the face.  To do that we need to find the height of each triangle and subtract.

 

Recall that Tan = opposite/adjacent.

 

In this case the adjacent is 800

Tan 27 = 0.509525

Tan 31 = 0.60086

 

Height for 27^o angle -->  0.509525 = h/800  --> h = 407.62 feet

Height for 31^o angle --> 0.60086 = h/800 --> h = 480.69 feet

 

Therefore the height of the face is 480.69 - 407.62 = 73.07 feet