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Date	November 2018	Marks available	6	Reference code	18N.2.AHL.TZ0.H_7
Level	Additional Higher Level	Paper	Paper 2	Time zone	Time zone 0
Command term	Find	Question number	H_7	Adapted from	N/A

Question

Boat A is situated 10km away from boat B, and each boat has a marine radio transmitter on board. The range of the transmitter on boat A is 7km, and the range of the transmitter on boat B is 5km. The region in which both transmitters can be detected is represented by the shaded region in the following diagram. Find the area of this region.

Markscheme

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

use of cosine rule (M1)

CÂB = arccos $\left( {\frac{{49 + 100 - 25}}{{2 \times 7 \times 10}}} \right) = 0.48276 \ldots \left( { = 27.660 \ldots ^\circ } \right)$ (A1)

C $\mathop {\text{B}}\limits^ \wedge$ A = arccos $\left( {\frac{{25 + 100 - 49}}{{2 \times 5 \times 10}}} \right) = 0.70748 \ldots \left( { = 40.535 \ldots ^\circ } \right)$ (A1)

attempt to subtract triangle area from sector area (M1)

area $= \frac{1}{2} \times 49\left( {2{\text{C}}\mathop {\text{A}}\limits^ \wedge {\text{B}} - {\text{sin}}\,{\text{2C}}\mathop {\text{A}}\limits^ \wedge {\text{B}}} \right)\, + \frac{1}{2} \times 25\left( {2{\text{C}}\mathop {\text{B}}\limits^ \wedge {\text{A}} - {\text{sin}}\,{\text{2C}}\mathop {\text{B}}\limits^ \wedge {\text{A}}} \right)$

= 3.5079… + 5.3385… (A1)

Note: Award this A1 for either of these two values.

= 8.85 (km²) A1

Note: Accept all answers that round to 8.8 or 8.9.

[6 marks]

Examiners report

[N/A]

Syllabus sections

Topic 3—Geometry and trigonometry » SL 3.2—2d and 3d trig

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