Question

Use the image to answer the question.

A triangle has an image of a tree superimposed on its opposite side.

A tree casts a shadow as shown in the image. If the tree is 34 feet tall, and the distance from the top of the tree to the top of the shadow is 47 feet, what is the angle formed from the top of the tree? Round your answer to the nearest whole degree.

(1 point)
The angle is approximately
°.

Answer 1

Let θ be the angle at the top of the tree. In the right triangle, cos θ = adjacent/hypotenuse = 34/47, so

θ = arccos(34/47) ≈ 43.7° ≈ 44° (to the nearest degree).

Answer: 44°.