Worksheets · Foundation and Higher

Bearings and geometric modelling

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Non-calculator · 3 marks
A map is drawn to a scale of 1 cm to 5 km.
(a) Two towns are 4.6 cm apart on the map. Work out the real distance between them. (2)
(b) A lighthouse is due south-east of a port. Write down the bearing of the lighthouse from the port. (1)
Question 2Non-calculator · 4 marks
From A, B is on a bearing of $055^\circ$ and C is on a bearing of $125^\circ$ . AB = AC = 9 km.
(a) Find angle BAC. (2)
(b) Find angle ABC. (2)
Question 3Calculator · 5 marks
A walker leaves $A$ and walks 8 km on a bearing of $040^\circ$ to $B$ . She then walks 6 km on a bearing of $130^\circ$ to $C$ .
(a) Work out the bearing of $C$ from $A$ . Give your answer to the nearest degree. (4)
(b) Write down the bearing of $A$ from $C$ . (1)

Answers and marks

(a) 23 km

(b) $135^\circ$

(a) $70$ °

(b) $55$ °

(a) $077^\circ$

P1 Showing angle $ABC = 90^\circ$ (from $130 - 40$ and the north lines being parallel).
P1 Angle $BAC$ from $\tan^{-1}\left(\frac{6}{8}\right)$ (or $AC = 10$ then sine or cosine).
P1 Adding their angle to $40^\circ$ .
A1 Correct answer: $077^\circ$ .

(b) $257^\circ$

Bearings and geometric modelling

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