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IB Mathematics: Applications and Interpretation SL · 12.10: Geometry & Trigonometry · 12.10.6

Name Date

Bearings Problem set A

Draw a diagram with north lines first. Give distances to 3 significant figures and bearings to the nearest degree, with three figures.

Difficulty: first skills applying them stretch

Skills

  1. Write down the bearing of the first point from the second point when the bearing of the second from the first is:

    6 km064°ABNN
    1. (a) 064°;
    2. (b) 281°;
    3. (c) 150°.

  2. P, Q and R are three buoys. Q is 8 km from P on a bearing of 063°. R is 11 km from Q on a bearing of 150°. Find the distance PR.

    8 km11 km?063°150°PQRNN

  3. Three villages P, Q and R: Q is 9 km from P on a bearing of 025°, and R is 7 km from Q on a bearing of 110°. Find the bearing of P from R, to the nearest degree.

    9 km7 km?025°110°PQRNN

In context

  1. A ship leaves harbour P and sails 18 nautical miles on a bearing of 075° to a lighthouse Q. It then sails 25 nautical miles on a bearing of 160° to an island R.

    18 nautical miles25 nautical miles?075°160°PQRNN
    1. (a) Find the distance PR.
    2. (b) Find the bearing on which the ship must sail from R to return directly to P, to the nearest degree.

  2. A drone flies 35 km from its base P on a bearing of 048°, then 28 km on a bearing of 300°. Find how far it is from P.

    35 km28 km?048°300°PQRNN

  3. Two coastguard stations X and Y are 15 km apart, with Y due east of X. A boat B is seen from X on a bearing of 035° and from Y on a bearing of 300°.

    15 km035°300°XYBNN
    1. (a) Find the distance of the boat from X.
    2. (b) Find the distance of the boat from Y.

Stretch

  1. A yacht leaves a marina P and sails 16 km on a bearing of 250° to Q. It then sails 12 km on a bearing of 170° to R.

    16 km12 km?250°170°PQRNN
    1. (a) Find the distance PR.
    2. (b) Find the bearing of P from R, to the nearest degree.

jmaths.xyz · AI SL · 12.10.6 Bearings