SOLUTION: The angle of elevation of the sun is 30 degrees. Find the length of the shadow cast by a 30 meter high steeple.

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Question 1105046: The angle of elevation of the sun is 30 degrees. Find the length of the shadow cast by a 30 meter high steeple.
Answer by Theo(13342) About Me  (Show Source):
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the angle of elevation of the sun is 30 degrees.
the steeple is 30 meters high.

the shadow of the steeple forms a right triangle where the opposite side is 30 meters and opposite the 30 degree angle.

the adjacent side to the 30 degree angle is the length of the shadow on the ground.

tangent of 30 degrees is opposite / adjacent = 30 / x.

x represents the length of the shadow.

multiply both sides of this equation by x to get x * tan(30) = 30.

divide both sides of this equation by tan(30) to get x = 30 / tan(30).

solve for x to get x = 51.96152423.

that's the length of the shadow.

the sketch of the problem looks like this:

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