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Date November 2016 Marks available 5 Reference code 16N.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

In a triangle ABC, AB = 4  cm, BC = 3  cm and B A ^ C = π 9 .

Use the cosine rule to find the two possible values for AC.

[5]
a.

Find the difference between the areas of the two possible triangles ABC.

[3]
b.

Markscheme

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

METHOD 1

let  AC = x

3 2 = x 2 + 4 2 8 x cos π 9    M1A1

attempting to solve for x     (M1)

x = 1.09 ,   6.43    A1A1

METHOD 2

let  AC = x

using the sine rule to find a value of C     M1

4 2 = x 2 + 3 2 6 x cos ( 152.869 ) x = 1.09    (M1)A1

4 2 = x 2 + 3 2 6 x cos ( 27.131 ) x = 6.43    (M1)A1

METHOD 3

let  AC = x

using the sine rule to find a value of B and a value of C     M1

obtaining B = 132.869 ,   7.131  and C = 27.131 ,   152.869      A1

( B = 2.319 ,   0.124 and C = 0.473 ,   2.668 )

attempting to find a value of x using the cosine rule     (M1)

x = 1.09 ,   6.43    A1A1

 

Note: Award M1A0(M1)A1A0 for one correct value of x

 

[5 marks]

a.

1 2 × 4 × 6.428 × sin π 9 and 1 2 × 4 × 1.088 × sin π 9      (A1)

( 4.39747 and 0.744833 )

let D be the difference between the two areas

D = 1 2 × 4 × 6.428 × sin π 9 1 2 × 4 × 1.088 × sin π 9    (M1)

( D = 4.39747 0.744833 )

= 3.65  (c m 2 )    A1

[3 marks]

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Topic 3— Geometry and trigonometry » SL 3.5—Unit circle definitions of sin, cos, tan. Exact trig ratios, ambiguous case of sine rule
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Topic 3— Geometry and trigonometry

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