# At 10 am on april 26, 2000, a building 300 feet high casts a shadow 50 feet long. What is the angle of the elevation of the sun?

I found:

Considering the diagram:

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To find the angle of elevation of the sun, we can use the tangent function. The tangent of an angle in a right triangle is equal to the length of the side opposite the angle divided by the length of the adjacent side.

In this scenario, the height of the building represents the side opposite the angle of elevation (the vertical side), and the length of the shadow represents the adjacent side (the horizontal side). Therefore, we can set up the equation:

[ \tan(\theta) = \frac{\text{height of building}}{\text{length of shadow}} ]

[ \tan(\theta) = \frac{300}{50} ]

[ \tan(\theta) = 6 ]

To find the angle ( \theta ), we need to take the arctangent (inverse tangent) of both sides:

[ \theta = \arctan(6) ]

Using a calculator, we find:

[ \theta \approx 80.54^\circ ]

Therefore, the angle of elevation of the sun at 10 am on April 26, 2000, is approximately ( 80.54^\circ ).

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