Question 1049345: A church spire 82 cm high cast a shadow 62 meters long. find the angle of elevation of the sun at that moment. Draw the diagram also.
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! The base of the right triangle is the length of the shadow: 62
The height of the church spiral is the long leg of the right triangle: 82
The other leg, the hypotenuse, goes from the end of the shadow to the top of the spire, this is the tangent and is the angle you want:
SOHCAHTOA Since we know the Opposite (the base or short leg) and the Adjacent (long leg) we apply TOA: Tangent = Opposite/Adjacent.
:
Tan(x) = 62/82 both are divisible by 2, simplify:
Tan(x) = 31/41
x = Tan^(-1)(41/31) this is the inverse tan, look for the tan^-1 or arctan key in your calculator (mine has a tan^-1 key)
x = Tan^-1(41/31) = 52.9 is your answer
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