SOLUTION: A man is standing 150 ft from the base of a tower. The angle is 62 degrees. How tall is the tower? We know that this is a right triangle. Can you find the hypotenuse if you kno

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Question 16962: A man is standing 150 ft from the base of a tower. The angle is 62 degrees. How tall is the tower? We know that this is a right triangle. Can you find the hypotenuse if you know the angles and only one side?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You can readily solve this problem using elementary trigonometry.
Knowing that the angle of elevation from the observer on the ground to the top of the tower is 62 degrees, and knowing that the observer is 150 feet from the base of the tower, you can use the tangent function to find the height, h, of the tower. In the right triangle formed by the tower (vertical leg = h) and the distance of the observer from the base of the tower (base of the right triangle = 150 ft.), the tangent of the angle of elevation , A, is given by:
tan%28A%29+=+h%2F150 Multiply both sides by 150.
h+=+%28150%29tan%28A%29 Angle A = 62 degs.
h+=+%28150%29tan%2862%29 Tan(62) = 1.88
h+=+%28150%29%281.88%29
h+=+282
The tower is 282 feet tall.