230k views
5 votes
A boy leaves station X on a bearing of 035' to station Y. which is 21km away. He then travels to another station Z on a bearing of 125 degrees . If Z is directly East of X, what is the distance from X to his present position?​

User Djunod
by
3.9k points

1 Answer

4 votes

9514 1404 393

Answer:

36.6 km

Explanation:

We assume the initial bearing of the boy is 35°. Then he will make a 90° turn to a heading of 125°. A diagram shows the distance of interest is the hypotenuse of a right triangle in which 35° is the angle opposite the side of length 21 km.

The relevant trig relation is ...

Sin = Opposite/Hypotenuse

sin(35°) = (21 km)/XZ

XZ = (21 km)/sin(35°) ≈ 36.61 km

The distance from X to Z is about 36.61 km.

_____

The attached diagram has the angles measured in the usual way for a Cartesian plane: CCW from the +x axis. This will correspond to bearing measures if we relabel the axes so that +x is North, and +y is East.

A boy leaves station X on a bearing of 035' to station Y. which is 21km away. He then-example-1
User Shoeb Mirza
by
3.4k points