Quick questions on Radial surveys and bearings for HSC Maths Standard 2

A true bearing is measured clockwise from north, in three digits, from $000\degree$ to $360\degree$.

A compass bearing uses a primary direction (N or S) followed by an acute angle, then E or W. For example, N$30\degree$E means start facing north and rotate $30\degree$ towards the east; S$40\degree$W means start facing south and rotate $40\degree$ towards the west.

If the bearing of $B$ from $A$ is $\theta$, then the bearing of $A$ from $B$ is $\theta + 180\degree$ (subtract $360\degree$ if the result exceeds $360\degree$, or equivalently subtract $180\degree$ when $\theta \geq 180\degree$).

A radial survey (also called a plane-table survey) records the distances and true bearings of several points from a single central station. It is the standard way to fix the positions of features around one observation point, and the data is given as a table or a diagram. Once plotted, every point sits at a known distance and bearing from the centre, so any two points and the centre form a triangle you can solve.

Suppose a surveyor at station $O$ records three points: $P$ at $040\degree$, $70$ m; $Q$ at $110\degree$, $80$ m; $R$ at $205\degree$, $60$ m. The task is to find the straight-line distance $PQ$. Here is how the plot and the solution build up.

Always use three digits: $075\degree$, not $75\degree$.

Always degrees, not radians.