Answer:
The angle of depression is 51°
Step-by-step explanation:
* Lets explain how to solve the problem
- The observer is 120 ft from the base of a television tower
∴ The horizontal distance between the observer and the base of the
tower is 120 ft
- The height of the tower is 150 ft
∴ The vertical distance from the base of the tower to its top is 150 ft
- The horizontal distance and the vertical distance formed the two
legs of a right triangle and the angle of depression is opposite to
the vertical distance and adjacent to the horizontal distance
# Look to the attached figure for more understanding
- To find the angle of depression use the tangent function to find it
∵ tan Ф = opposite/adjacent
∵ The length of the opposite is 150 ft
∵ The length of the adjacent is 120 ft
∵ The angle of depression is Ф
∴ tan Ф = 150/120 = 5/4
- Use the inverse of tan to find Ф
∵ Ф = [tex]tan^{-1}\frac{5}{4}[/tex]
∴ Ф = 51°
* The angle of depression is 51°
