Question

A 5.8-ft fence is 15.431 ft away from a plant in the direction of the sun. It is observed that the shadow of the fence extends exactly to the bottom of the plant. (See drawing) Find θ, the angle of elevation of the sun at that time. Round the measure of the angle to the nearest tenth of a degree when necessary.

Answer 1

Answer: The measure of the angle of elevation would be 20.6°.

Explanation:

Since we have given that

Length of fence = 5.8 feet

Distance between fence and plant in the direction of sun = 15.431 feet

We need to find the angle of elevation of the sun at that time.

We will use "Tangent formula";

`\tan \theta=(Perpendicular)/(base)\\\\\tan \theta=(5.8)/(15.431)\\\\\tan \theta=0.375\\\\\theta=\tan^(-1)(0.375)\\\\\theta=20.59^\circ`

Hence, the measure of the angle would be 20.6°.