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Date	May 2019	Marks available	3	Reference code	19M.2.SL.TZ2.S_3
Level	Standard Level	Paper	Paper 2	Time zone	Time zone 2
Command term	Find	Question number	S_3	Adapted from	N/A

Question

The following diagram shows the quadrilateral ABCD.

AB = 6.73 cm, BC = 4.83 cm, BĈD = 78.2° and CD = 3.80 cm.

Find BD.

[3]

The area of triangle ABD is 18.5 cm². Find the possible values of θ.

[4]

Markscheme

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

choosing cosine rule (M1)

eg ${c^2} = {a^2} + {b^2} - 2ab\,{\text{cos}}\,C$

correct substitution into RHS (A1)

eg ${4.83^2} + {3.80^2} - 2 \times 4.83 \times 3.80 \times {\text{cos}}\,78.2$ , $30.2622$ ,

${4.83^2} + {3.80^2} - 2\left( {4.83} \right)\left( {3.80} \right) \times {\text{cos}}\,1.36$

5.50111

5.50 (cm) A1 N2

[3 marks]

correct substitution for area of triangle ABD (A1)

eg $\frac{1}{2} \times 6.73 \times 5.50111\,{\text{sin}}\,\theta$

correct equation A1

eg $\frac{1}{2} \times 6.73 \times 5.50111\,{\text{sin}}\,\theta = 18.5$ , ${\text{sin}}\,\theta = {\text{0}}{\text{.999393}}$

88.0023, 91.9976, 1.53593, 1.60566

θ = 88.0 (degrees) or 1.54 (radians)

θ = 92.0 (degrees) or 1.61 (radians) A1A1 N2

[4 marks]

Examiners report

[N/A]

Syllabus sections

Topic 3— Geometry and trigonometry » SL 3.2—2d and 3d trig, sine rule, cosine rule, area

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Find the size of angle ${\text{B}}\mathop {\text{A}}\limits^ \wedge {\text{C}}$ .
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Find the size of angle ${\text{C}}\mathop {\text{A}}\limits^ \wedge {\text{D}}$ .
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Find the size of angle ${\text{A}}\mathop {\text{C}}\limits^ \wedge {\text{D}}$ .
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Calculate the angle of elevation of T from, M, the midpoint of the side AC.
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16N.2.SL.TZ0.T_5c:
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16N.2.SL.TZ0.T_5e:
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