Question

Find the angle of elevation of the sun from the ground when a tree that is 18 ft tall casts a shadow 25 ft long. Round to the nearest degree.

Answer 1

36°

Explanation:

Let
`\theta` be the angle of elevation. The side opposite of
`\theta` will be the height of the tree, which is 18ft, and the side adjacent to
`\theta` will be the length of the shadow, which is 25ft. Because these two lengths are known, then we should use the tangent ratio to determine the measure of the angle of elevation:

`\displaystyle \tan\theta=\frac{\text{Opposite}}{\text{Adjacent}}=(18)/(25)\biggr\\\\\\\theta=\tan^(-1)\biggr((18)/(25)\biggr)\approx36^\circ`

Therefore, the angle of elevation is about 36°.