Question

If you're good at trig pls help meeeeeee

Pls show full working out and round answer to nearest kilometre

Answer 1

*flashbacks to honors trig in 9th grade*

...Anyway. We're given that the bearing from A to C is
`330^\circ,` so that means that the counterclockwise angle from the north to C is
`30^\circ.` Therefore,
`\angle BAC=50^\circ+30^\circ=80^\circ.`

Now, we apply the law of cosines:

`BC^2&=AC^2+BC^2-2(AC)(BC)\cos\angle BAC`

`BC^2&=65^2+135^2-2(65)(135)\cos 80^\circ=22450-17550\cos 80^\circ`

`\boxed{BC\approx 139\text{ km}}.`