Find to the nearest degree the measure of the angle of elevation of the sun when a vertical post 15 feet high casts a shadow 20 feet long.

Expert Answers

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To solve, refer to the figure below.

In the figure, `theta` is the angle of elevation of the sun. To determine its value, use the tangent function since the length of the sides opposite and adjacent to theta are known.

`tan theta=(opposite)/(adjacent )`

`tan theta=15/20`

`tan theta=3/4`

`theta=tan^(-1)3/4`

`theta=36.86989764^o`

Rounding off to the nearest degree, it becomes:

`theta=37^o`

Hence, the angle of elevation of the sun is 37 degrees.

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