Precalc question

Question

A surveying crew is tasked to measure the height of a mountain. From a point on level ground, they measure the angle of elevation to the top of the mountain as 21.6°. They move 500m closer and find the angle of elevation to the top of the mountain is now 35.5°. How high is the mountain? (round your answer to the nearest meter)

Answer 1

Let the distance from the second point to a point under the mountain peak be x. Let y be the height.

tan(21.6°) ≈ 0.38 = y/(500+x)

tan(35.5°) ≈ 0.71 = y/x --> x = y/0.71 = 1.4y

0.38(500+1.4y) =y

190 + 0.532 y = y

0.468y = 190

y = 405.98 ≈ 406 m