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IB Maths AA SL 3.2 Triangle Trigonometry

IB Maths AA SL 3.2 Triangle Trigonometry
IB Mathematics: analysis and approaches guide, first assessment 2021

Practise choosing and applying right-triangle ratios, sine rule, cosine rule and the area formula to determine sides, angles or exact expressions from labelled diagrams.

How this is tested

  • choose a right-triangle ratio or sine rule when a known opposite side-angle pair is available
  • apply cosine rule for three sides or two sides and their included angle, preserving exact values
  • use area = 1/2 ab sin C with the included angle and combine it with another triangle relation

Question 7

[Maximum number: 14]

Consider a triangle PQR where PR=3, QR=2 and PR^Q=60∘\mathrm{P} \hat{\mathrm{R}} \mathrm{Q}=60^{\circ}.

Figure for Question 7 — IB Maths AA SL

Question 7(a)

(a)

Find PQ .

Now consider a general triangle ABC where AC=x+2, BC=3 x-1 and ACB^=60∘\mathrm{A} \hat{\mathrm{C} B}=60^{\circ}.

Figure for Question 7(a) — IB Maths AA SL
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Question 7(b)

(b)

Show that AB=7x2−7x+7\mathrm{AB}=\sqrt{7 x^{2}-7 x+7}.

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Question 7(c)

(c)

Given that AB=7,

[ 6 ]

Question 7(c)(ii)

(i)

find the area of triangle ABC .

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