Question

There are 3 boats, P, Q and R. Boat Q is 7km from boat P on a bearing of 327. boat R is 15km from boat P on a bearing of 041. Find the distance between boats Q and R to 1dp?

I'm not sure where to begin with this and I'm struggling to understand the bearings

Answer 1

`color(blue)(14.7color(white)(88) "km")`

Explanation:

From the diagram we can see that we need to find the line QR

First we calculate angle at P, this is:

`33^@+41^@=74^@`

Using the Cosine Rule:

`bb((QR))^2=(bb(PQ))^2+(bb(PR))^2-2(bb(PQ))(bb(PR))*cos(bb(P))`

`(bb(QR))^2=(7)^2+(15)^2-2*(7)(15)*cos(74^@)`

`(bb(QR))^2=49+225-210*cos(74^@)`

`(bb(QR))^2=274-210*cos(74^@)`

`bb(QR)=sqrt(274-210*cos(74^@))=color(blue)(14.7color(white)(88) "km")`

When solving problems like this, it is best to start with the point that the bearings are given from and mark the vertical line representing NORTH.

This is where all the measurement are taken from. Angles are measured clockwise from the vertical. The angle `33^@` was arrived at by:

`360^@-327^@=33^@`

As a note:

Bearings are given as 3 figures, that is why we have angles like 041. This is just `41^@`

Hope this helps.