Algebra II
posted by Lyndsie on .
An airplane leaves airport A and flies 200 km. At this time its bearing from Airport B, 250 km to the west, is 120 degrees. How far is the airplane from B?

let the plane's position be P
so in triangle ABP, angle A = 30° ( a bearing of 120 = 90+30)
let's find angle P
sinP/250 = sin 30/200
(case 1)
angle P = 38.682
then angle A = 113.328°
BP/sin113.328 = 200/sin30
BP = 372.63 km
case 2
angle P = 141.318
then angle A = 8.682°
BP/sin8.682 = 200/sin30
BP = 60.38 km
both answers make sense, since the triangle results in the "ambiguous case" 
1. A passenger in an airplane at an altitude of 10 km sees two towns to the east of the plane. The angle of depression to town A is 28o and the angle of depression to town B is 55o. How far apart are the two towns?