SOLUTION: From the helicopter 3000 ft. directly over one base of a
mountain the angle of depression to the base on the other side is
49 degrees 12 minutes. How long a tunnel is needed to
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Question 1196432: From the helicopter 3000 ft. directly over one base of a
mountain the angle of depression to the base on the other side is
49 degrees 12 minutes. How long a tunnel is needed to go through the mountain?
Answer by amoresroy(361) (Show Source): You can put this solution on YOUR website!
Given:
Angle of depression = 49 degrees 12 minutes = 49.2 ⁰ ( given 60 minutes/degree)
Height of triangle is 3,000 meters
Let L = the length of a tunnel that is needed to go through the mountain.
Since L is perpendicular to the height, we have
Equation:
Tan (49.2) = 3,000/L
L = 3,000/Tan (49.2)
L = 3,000/1.1585
L = 2,589.6
Answer
The length of a tunnel that is needed to go through the mountain is 2,589.6 feet.
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