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Date	May 2015	Marks available	2	Reference code	15M.2.hl.TZ2.1
Level	HL only	Paper	2	Time zone	TZ2
Command term	Find	Question number	1	Adapted from	N/A

Question

In triangle ${\text{ABC}}$ , ${\text{AB}} = 5{\text{ cm}}$ , ${\text{BC}} = 12{\text{ cm}}$ and ${\rm{A\hat BC}} = 100^\circ$ .

Find the area of the triangle.

[2]

a.

Find $AC$ .

[2]

b.

Markscheme

$A = \frac{1}{2} \times 5 \times 12 \times \sin 100^\circ$ (M1)

$= 29.5{\text{ (c}}{{\text{m}}^2}{\text{)}}$ A1

[2 marks]

a.

${\text{A}}{{\text{C}}^2} = {5^2} + {12^2} - 2 \times 5 \times 12 \times \cos 100^\circ$ (M1)

therefore ${\text{AC}} = 13.8{\text{ (cm)}}$ A1

[2 marks]

Total [4 marks]

b.

Examiners report

[N/A]

a.

[N/A]

b.

Syllabus sections

Topic 3 - Core: Circular functions and trigonometry » 3.7 » Area of a triangle as

$\frac{1}{2}ab\sin C$ .

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