Question

A 15 foot tall flag pole casts a shadow that is 27 feet long. What is the angle ofelevation to the sun?

Answer 1

Before we start answering, let's draw a scheme with our measures

As you can see, the shadow and the pole form a right triangle, where A is the angle of elevation to the sun.

Using trigonometric relations, we know that the ratio between the opposite leg to an angle by the adjacent leg to the same angle is equal to the tangent of said angle. Then, we can create the following equation for our angle A:

`\tan A=(15)/(27)`

Then, Angle A is

`A=\tan ^(-1)(15)/(27)=29.0546040991\ldots\approx29^o`