Solve.
-A plane flying a straight course observes a mountain at a bearing of 30.1° to the right of its course. At that time the plane is 6 km from the mountain. A short time later, the bearing to the mountain becomes 40.1°. How far is
The plane from the mountain when the second bearing is taken (to the nearest tenth of a km)?
A) 3.1 km
B) 7.7 km
C) 8.8 km
D) 4.7 km

Question

Quizplus · Accepted Answer

To solve this problem, we can use trigonometry, specifically the Law of Sines, in the triangle formed by the plane's initial position, its position when the second bearing is taken, and the mountain. The angle change is 40.1° - 30.1° = 10°. This angle, along with the initial distance of 6 km from the mountain, allows us to set up the equation sin(10°)/d = sin(40.1°)/6, where d is the distance from the mountain when the second bearing is taken. Solving for d gives approximately 4.7 km.

Solve. -A Plane Flying a Straight Course Observes a Mountain at at a Bearing