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 ft., how far is the bird (B) from the plane (P)?

A diagram is shown with two parallel lines cut by a transversal. One angle is marked 33 degrees, one side is marked 7000 and another side is marked x.

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 ft., how far is the bird (B) from the plane (P)?

A diagram is shown with two parallel lines cut by a transversal. One angle is marked 33 degrees, one side is marked 7000 and another side is marked x.

zpupster · Answer

start by getting hypotenuse
sin = O/H
sin33= 7000/H
H=7000/sin33

then use pythagorean
7000^2 + x^2 = H^2  plug you H from Above and solve