Matt measures the angle of elevation of the peak of a mounta

Matt measures the angle of elevation of the peak of a mountain as 35 degree. Susie, who is 1200 feet closer on a straight level path, measures the angle of elevation as 42 degree. How high is the mountain?

Solution

y = (1200 + x)(tan 35°)

y = (x)(tan 42°)

(1200 + x)(tan 35°) = (x)(tan 42°)

840.25 + 0.7002x = 0.900x

x = 4197.13 (distance from Susie to the point directly perpendicular to the peak)

Matt is 4197.13 + 1200 = 5397.13
from the point directly perpendicular to the peak

tan 35° = y/5397.13

y = 3,779.11 ft (height of the mountain)

or from Susie\'s point of view

tan 42° = y/4197.13

y= 3,779.11 ft (height of the mountain)