Question

An observer is 120 ft from the base of a television tower, which is 150 ft tall. Find the angle of depression at the top of the tower. Round to the nearest degree.

Answer 1

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 = $tan^{-1}\frac{5}{4}$

∴ Ф = 51°

* The angle of depression is 51°