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Date May 2018 Marks available 1 Reference code 18M.1.SL.TZ1.T_8
Level Standard Level Paper Paper 1 (with calculator from previous syllabus) Time zone Time zone 1
Command term Draw and Label Question number T_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]
a.

Find the size of angle APB.

[3]
b.

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

[2]
c.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

(A1) (C1)

[1 mark]

a.

40 sin APB = 30 sin 48      (M1)(A1)

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

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

[3 marks]

b.

180 − 48 − 82.2473…     (M1)

49.8°  (49.7526…°)     (A1)(ft)  (C2)

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

[2 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 3— Geometry and trigonometry » SL 3.2—2d and 3d trig, sine rule, cosine rule, area
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Topic 3— Geometry and trigonometry » SL 3.3—Applications: angles of elevation and depression, bearings
Topic 3— Geometry and trigonometry

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