Question

A cellular telephone tower that is 300 feet tall is placed on top of a mountain that is 1100 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? (Round your answer to two decimal places.)

Answer 1

Angle of depression=2.17°

Explanation:

Step 1: Determine the height of the tower relative to the cell phone user

Height of tower above sea level=Height of mountain above sea level+height of tower on top of the mountain

where;

Height of mountain above sea level=1,100 feet

Height of tower on top of the mountain=300 feet

replacing;

Height of tower above sea level=(1,100+300)=1,400 feet

Height of cell phone user above sea level=400 feet

Height of the tower relative to the cell phone user=Height of tower above sea level-height of cell phone user above sea level

where;

height of tower above sea level=1,400 feet

height of cell phone user above sea level=400 feet

replacing;

Height of the tower relative to the cell phone user=(1,400-400)=1,000 feet

Step 2: Determine the angle of depression

Tan∅=Horizontal distance from tower to cell phone user/vertical distance between top of tower and cell phone user

where;

Horizontal distance from tower to cell phone user=5 miles

1 mile=5,280 feet, (5×5,280)=26,400 feet

Vertical distance between top of tower and cell phone user=1,000 feet

replacing;

Tan∅=26,400/1,000

Tan∅=26.4

∅=Tan^(-1)(26.4)

∅=87.83°

Angle of depression=90-∅=90-87.83=2.17°

Angle of depression=2.17°