Question

A cell phone tower is 120 ft tall. The pole creates a 74 ft shadow. What is the angle of elevation of the sun? Round your answer to the nearest degree

Answer 1

The angle of elevation is 58 degrees

Solution:

Given that cell phone tower is 120 feet tall

The tower creates a 74 feet shadow

To find: angle of elevation of sun

The cell phone tower and base ( shadow) forms a right angled triangle

The figure is attached below

ABC is right angled triangle

AC = height of tower = 120 feet

AB = length of shadow = 74 feet

We have to find the angle of elevation

By definition of tan,

$tan \theta = \frac{height}{base}\\\\tan \theta = \frac{AC}{AB}\\\\tan \theta = \frac{120}{74}\\\\tan \theta = 1.621\\\\\theta = tan^{-1}{1.621}\\\\\theta = 58.32 \approx 58$

Thus angle of elevation is 58 degrees