Question

A cellular telephone tower that is 150 feet tall is placed on top of a mountain that is 1200 feet above sea level. What is the angle of depression from the top of the tower to a cell phone user who is 5 horizontal miles away and 400 feet above sea level

Answer 1

Answer:

87.9391 degrees

Step-by-step explanation:

The top of the cellular phone tower will be at 1200 + 150 = 1350 feeet above sea level.

The cell phone user is at 400 feet above sea level, so the difference of height between the cellular phone tower and the cell phone user is 1350 - 400 = 950 feet.

The horizontal distance between then is 5 miles, which is 5 * 5280 = 26400 feet.

To calculate the angle, we need to imagine a triangle, where the angle is at the top of the tower, the adjacent cathetus is 950 feet, and the opposite cathetus is 26400 feet.

The relation between opposite cathetus and adjacent cathetus is the tangent, so:

tan(angle) = 26400 / 950 = 27.7895

angle = 87.9391 degrees

Answer 2

Answer:

angle of depression = 2.1⁰

Step-by-step explanation:

1 mile = 5280 ft

Hence angle of depression = 90 - ∅

Where ∅ is angle of depression

Tan ∅ = (5 x 5280)/ 950

∅ = Tan₋¹ (27.789474) = 87.9⁰

Hence angle of depression = 90 - 87.9 = 2.1⁰