Question 787092: 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. They move 500 m closer and find that the angle of elevation to the top of the mountain is now 35 degrees 30 minutes. How high is the mountain?
Answer by xinxin(76)   (Show Source):
You can put this solution on YOUR website! I cannot draw/copy&paste graphs in the answer field...
Well the statement shows a right angle whose height is the height of the mountain. The two mentioned angles are inside this right angle. One of them is 21 degrees 40 minutes,an angle that is opposite to the height; the other is formed when you draw a line connecting two points (one is on the base , the other is on the hypotenuse), and it is 35 degrees 30 minutes.
To find out the value of height you will need to solve a linear system. In the solution H = Height, B = Base:
tan (21 degrees 40 minutes) = H/B = 0.4
tan (35 degrees 30 minutes) = H/(B-500) = 0.7
Solve for H, get H = 466.7
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