Question

An observer (O) spots a plane (P) taking off from a local airport and flying at a 33° angle

horizontal to her line of sight and located directly above a tower (1). The observer also notices a

bird (B) circling directly above her. If the distance from the plane(P) to the tower () is 7,000 feet,

how far is the bird (B) from the plane (P)? Round to the nearest whole number.

B

х

P

7000

1

1

1

33°

A

Answer 1

Answer: 10,779 feets

Explanation:

From the sketch attached ;

∠POT is the Angle of elevation = 33°

Height of tower = 7000 Feets

Taking the triangle POT

WHERE PT = 7000 Feets (Opposite)

Distance (d) between the bird and plane is the ADJACENT,

NOTE: (BP = OT = d)

Taking the tangent of the angle of elevation;

Tan Θ = opposite / Adjacent

Tan 33° = 7000 / d

Cross multiply

d × 0.6494075 = 7000

d = 7000 / 0.6494075

d = 10779.054 = 10,779 feets