A 90-foot-tall tree casts a shadow 22 feet long. Find the angle of elevation of the sun to the nearest degree .

Answer 1

A very popular trigonometry problem....Elevation of the Sun.

Answer 2

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22

The tree height (90) and shadow length (22) for two legs of the right triangle. We can draw the hypotenuse from the top of the tree to the end of the shadow. The angle of elevation is E as shown in the diagram.

To find E we are going to use the trigonometric function for a right triangle.

We have the opposite side (90) and the adjacent side (22) to the angle E, so we will use the tangent function to find E.

tan (E) = opposite side/adjacent side = 90/22 = 4.09

arctan (tan E) = arctan(4.09)

E = arctan(4.09) = 76.26 degrees