Hello, Ruscur!

A car leaves a camp site and travels in the direction of S 65° E for 8.2 km.

It then heads due south for 6.7 km to reach a waterhole.

a) How far is the waterhole from the camp site?

b) What is the bearing of the waterhole from the camp site? First, we need a sketch . . . Code:

A N
* 8.2 :
:. * 65°:
: 65° * :
: . * B
: . 115°|
: . |
: . |
S . | 6.7
. |
. |
. |
.|
* C

The car goes 8.2 km from to

. .

Then it goes 6.7 km south to

. .

Law of Cosines: .

(a) Therefore: .

Law of Cosines: .

Hence: .

Therefore: .

The bearing is: .