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 (T). The observer also notices a bird (B) circling directly above her. If the distance from the plane(P) to the tower (T) is 7,000 feet, how far is the bird (B) from the plane (P)? Round to the nearest whole number.

Answer 1

Answer: 10,779 feet

Step-by-step explanation: I just took the test and got it right

Answer 2

the distance of the Bird (B) from the plane (P) is = 10779 ft

Explanation:

From the given information:

a diagrammatic representation is attached below for better understanding and solution to the question.

From the diagram;

Let the Bird (B) be represent as A

The plane (P) be represented by B

The observer be represented by O

and the tower T be represented by C

we will see that:

`\overline {AB} \ \| \ \overline {OC}`

Also;

`\angle ABO = \angle BOC = 33^0`

AO = BC = 7000

Let consider the trigonometry of triangle BAO

tan θ = opposite/adjacent

tan 33° = 7000/x

0.6494 = 7000/x

x = 7000/0.6494

x = 10779.18

x = 10779 ft ( to the nearest whole number)

Thus; the distance of the Bird (B) from the plane (P) is = 10779 ft