18M.1.SL.TZ1.T_8

pestleMathematicsAASLPaper 118M· sl-3-2-2d-and-3d-trig-sine-rule-cosine-rule-areasource ↗

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 / solution

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

(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]