SOLUTION: A man measures the angle of elevation to the top of a mountain to be 12 degrees. He drives 7 miles closer and finds the angle of elevation to be 37 degrees. How high is the mountai

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Question 1034720: A man measures the angle of elevation to the top of a mountain to be 12 degrees. He drives 7 miles closer and finds the angle of elevation to be 37 degrees. How high is the mountain?
Found 2 solutions by addingup, MathTherapy:
Answer by addingup(3677)   (Show Source): You can put this solution on YOUR website!
Use the tan function on both angles, and solve the equation, but first convert miles to feet:
7 miles = 36960 (1 mile = 5280 feet)
height/(length+36960)= tan 12
height/length = tan 37
height/(length+36960)= 0.21256
height/length = 0.7536
Height of the mountain:
h= (36960*0.7536*0.21256)/(0.7536-0.21256) = 10942.71 feet
Hopefully I have it right. Please let me know if I don't. Learning is a continuous cycle.
John

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
A man measures the angle of elevation to the top of a mountain to be 12 degrees. He drives 7 miles closer and finds the angle of elevation to be 37 degrees. How high is the mountain?
With y being the distance from where he walked to, to the base of the building, the following proportion can be set up:



 



3.545193y = 7 + y -------- Cross-multiplying

3.545193y – y = 7

2.545193y = 7

, or 2.750283



Now, height of mountain =  = 

If familiar with the Law of Sines, you can also use this to find the height. As a matter of fact, this method is easier. 

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