A boat sails 8 km north from P to Q and then sails 6 km west from Q to R. Calculate the bearing of R from P. Give your answer to the nearest degree.

Analyze the question: The boat goes 8 km north (P to Q), then 6 km west (Q to R). We need the bearing of R from P, measured clockwise from North at P.

Concept: A bearing is measured clockwise from North, written with three digits. R is north and west of P, so it lies in the north-west quadrant. Its bearing will be between 270° and 360°.

Solution:

Set P as the origin. Then Q is 8 km directly north of P, and R is 6 km west of Q.

In right-angled triangle PQR (right angle at Q):

tan θ = opposite/adjacent = QR/PQ = 6/8 = 0.75

θ = tan⁻¹(0.75) ≈ 36.87° ≈ 37°

θ is the angle between PQ (the north line) and PR, measured toward the west. So R is 37° west of north.

Bearing of R from P = 360° − 37° = 323°

Check against the options:

• 037° would mean R is north-east of P, which is wrong because the boat went west.
• 053° is also north-east, so it is wrong.
• 217° is south-west, so it is wrong.
• 323° is north-west, which matches.

Exam tip: Sketch a quick diagram and decide the quadrant first. North then west means a bearing between 270° and 360°. Find the acute angle from the north line, then subtract it from 360°. This quickly eliminates the wrong options.