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,
[tex]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[/tex]
Thus angle of elevation is 58 degrees
