Question

A 20 ft flag pole casts a shadow 32 ft long. What is the angle of elevation of the sun?

Answer 1

The angle of elevation of the sun is 32°

Explanation:

Right Triangles

The flagpole and the ground form a right angle (90°). In triangles with right angles, the trigonometric ratios are satisfied.

Each acute angle has an adjacent leg and an opposite leg. The tangent ratio relates to both legs.

`\displaystyle \tan x=\frac{\text{opposite leg}}{\text{adjacent leg}}`

The opposite leg to angle x is 20 ft and the adjacent leg is 32 ft, thus:

`\displaystyle \tan x=(20)/(32)=0.625`

Calculate x by using the inverse tangent:

`x=\arctan 0.625`

`x=32^\circ`

The angle of elevation of the sun is 32°