ONE
    Númas
    ← Back to the programme
    IBHardGeometry & Trigonometry7–9

    Distance and Bearing Back to Harbour

    Distância e Rumo de Regresso ao Porto

    A boat leaves harbour H and sails 12 km on a bearing of 040^\circ to a buoy B. It then sails 9 km on a bearing of 130^\circ to a point C. Find the distance HC and the bearing of C from H, to the nearest degree.

    Compare the two bearings: their difference tells you the angle the boat turned through, and therefore the shape of triangle HBC. For the bearing of C from H, find the angle between HB and HC first, then remember that bearings are measured from north.

    Solution

    Step 1 of 10

    1. 1.The bearings differ by 130^\circ - 40^\circ = 90^\circ, so the second leg turns the boat through a right angle and triangle HBC has a right angle at B.