A, B and C are three towns. The bearing of B from A is 045 degrees and the bearing of C from A is 150 degrees. The distance AB is 10km and the distance AC is 15km. Calculate the distance BC.

Here's a step-by-step solution to the problem:

Given:

• Village (V) to another village (H): $x$ km on a bearing of $250^\circ$.
• Village (H) to town (T): $\frac{4}{3}x$ km on a bearing of $340^\circ$. (Note: The question text states $\frac{2}{3}x$ km, but the student's diagram and calculations consistently use $\frac{4}{3}x$ km. We will proceed with $\frac{4}{3}x$ km as per the provided solution steps.)
• Village (V) to town (T): 10 km.

We will use the convention