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Date November 2010 Marks available 3 Reference code 10N.2.sl.TZ0.6
Level SL only Paper 2 Time zone TZ0
Command term Find Question number 6 Adapted from N/A

Question

The following diagram shows the triangle ABC.


The angle at C is obtuse, AC=5 cm, BC=13.6 cm and the area is 20 cm2 .

Find AˆCB .

[4]
a.

Find AB.

[3]
b.

Markscheme

correct substitution into the formula for the area of a triangle     A1

e.g. 12×5×13.6×sinC=20 , 12×5×h=20

attempt to solve     (M1)

e.g. sinC=0.5882 , sinC=813.6

ˆC=36.031 (0.6288 radians)     (A1)

AˆCB=144 (2.51 radians)     A1     N3

[4 marks]

a.

evidence of choosing the cosine rule     (M1)

correct substitution     A1

e.g. (AB)2=52+13.622(5)(13.6)cos143.968

AB=17.9     A1    N2

[3 marks]

b.

Examiners report

Part (a) was well done with the majority of candidates obtaining the acute angle. Unfortunately, the question asked for the obtuse angle which was clearly stated and shown in the diagram. No matter which angle was used, most candidates were able to obtain full marks in part (b) with a simple application of the cosine rule.

a.

Part (a) was well done with the majority of candidates obtaining the acute angle. Unfortunately, the question asked for the obtuse angle which was clearly stated and shown in the diagram. No matter which angle was used, most candidates were able to obtain full marks in part (b) with a simple application of the cosine rule.

b.

Syllabus sections

Topic 3 - Circular functions and trigonometry » 3.6 » The cosine rule.
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