Question

The pilot of an airplane flying at an elevation of 5000 feet sights two towers that are 300 feet apart. If the angle of depression to the tower closer to him is 30, determine the angle of depression to the second tower.

Answer 1

29.2°

Explanation:

From diagram (b)

Tan θ= opp/adj

Where θ = 30°

opp = 5000ft

adj = ?

tan 30° = 5000/x

x tan30° = 5000

x = 5000/tan 30

x = 5000/0.577

x = 8665.5ft

From diagram c

tan θ = opp/adj

Where θ = ?

opp = 5000

adj = 300+x

x= 8665.5

tan θ = 5000/300+8665.5

tan θ = 5000/8965.5

tan θ = 0.55769

θ = arch tan 0.55769

θ = 29.147

θ= 29.2°

Answer 2

Answer: 29.2 degree

Explanation:

Given data:

Elevation of the pilot = 50,000 feet

Elevation of the two towers = 300 feet apart.

Depression of closer tower = 30

Solution:

The angle of depression to the second tower is x

tanx = 5000/(5000*√(3)+300)

x=29.2

Therefore the angle of depression of the second tower is at 29.2 degree