Pre calculus?

Question

To measure the height of a mountain, a surveyor takes two sightings of the Pear at a distance 900 meters apart on a direct line to the mountain. The first observation results in an angle of elevation of 47 degrees, whereas the second results in an angle of elevation of 35 degrees. If the transit is 2 meters high, what is the height of the mountain???? 

Answer 1

Given:
Distance Between Sightings = 900 m.
First Observation Angle, Θ = 47°
Second Observation Angle, Φ = 35²
Height of Transit, y = 2 m.
Distance from Second Observation to Mountain = x
Distance from First Observation to Mountain = x - 900
Height of Mountain = h




Tan 35 = (h - 2) / x
0.7002 = (h - 2) / x
x = (h - 2) / 0.7002


Tan 47 = (h - 2) / (x - 900)
1.0724 = (h - 2) / (x - 900)
x - 900 = (h - 2) / 1.0724)
x = 900 + [(h - 2) / 1.0724]
x = [900(1.0724) / 1.0724] + [(h - 2) / 1.0724]
x = (965 + h - 2) / 1.0724
x = (963 + h) / 1.0724

x = (h - 2) / 0.7002, so

(h - 2) / 0.7002 = (963 + h) / 1.0724
1.0724(h - 2) = 0.7002(963 + h)
1.0724h - 2.148 = 674.29 + 0.7002h
1.0724h - 0.7002h = 674.29 + 2.148
0.3722h = 676.44
h = 676.44 / 0.3722
h = 1817.4  m
 

Height of Mountain = 1817.4 m.G