Question

Airplane A is flying directly toward the airport which is 30 miles away. The pilot notices Airplane B 40 degrees to her right. Airplane B is also flying directly toward the airport. The pilot of Airplane B calculates that Airplane A is 30 degrees to his left. Based in that information, how far is Airplane B from the airport?

Answer 1

We have used the usual convention that the side opposite an angle is named using the lower-case letter naming the angle. Here, the angles are named by the airplane designator (A or B).

Answer 2

9514 1404 393

Answer:

38.6 mi

Explanation:

The law of sines applies.

b/sin(B) = a/sin(A)

a = b(sin(A)/sin(B)) = (30 mi)sin(40°)/sin(30°)

a ≈ 38.6 mi

Airplane b is about 38.6 miles from the airport.

_____

We have used the usual convention that the side opposite an angle is named using the lower-case letter naming the angle. Here, the angles are named by the airplane designator (A or B).