Question

What is the angle of elevation of the sun if a 45 foot tall flagpole casts a 22 foot long shadow?

Answer 1

the angle Ф is 63.9 degrees.

Explanation:

A right triangle describes this situation. The height of the triangle is 45 ft and the base is 22 ft. The ratio height / base is the tangent of the angle of elevation and is tan Ф. We want to find the angle Ф:

opp

tan Ф = ---------- = 45 / 22 = 2.045.

adj

Using the inverse tangent function on a calculator, we find that the angle Ф is 63.9 degrees.