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Date	May 2018	Marks available	1	Reference code	18M.1.sl.TZ1.8
Level	SL only	Paper	1	Time zone	TZ1
Command term	Label and Draw	Question number	8	Adapted from	N/A

Question

Two fixed points, A and B, are 40 m apart on horizontal ground. Two straight ropes, AP and BP, are attached to the same point, P, on the base of a hot air balloon which is vertically above the line AB. The length of BP is 30 m and angle BAP is 48°.

Angle APB is acute.

On the diagram, draw and label with an x the angle of depression of B from P.

[1]

Find the size of angle APB.

[3]

Find the size of the angle of depression of B from P.

[2]

Markscheme

(A1) (C1)

[1 mark]

\(\frac{{40}}{{{\text{sin APB}}}} = \frac{{30}}{{{\text{sin 48}}^\circ }}\) (M1)(A1)

Note: Award (M1) for substitution into sine rule, (A1) for correct substitution.

(angle APB =) 82.2° (82.2473…°) (A1) (C3)

[3 marks]

180 − 48 − 82.2473… (M1)

49.8° (49.7526…°) (A1)(ft) (C2)

Note: Follow through from parts (a) and (b).

[2 marks]

Examiners report

[N/A]

Syllabus sections

Topic 5 - Geometry and trigonometry » 5.3

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