2022 SJI P2 Q6

2022 SJI P2 Q6

IB Year 5 | Grade 11
8 marks

Consider a triangle \(ABC\), where \(AB=1\text{ cm}\), \(B\widehat AC=\theta\text{ rad}\) and \(A\widehat BC=\dfrac34\pi\text{ rad}\).

  1. Show that \(AC=\dfrac1{\cos\theta-\sin\theta}\).[4]
  2. Given that the area of triangle \(ABC\) is \(\dfrac74\text{ cm}^2\), find the value of \(\theta\) and length of \(AC\).[4]

Solution:

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Answer:(a) Shown (b) \(\theta=0.661\text{ rad},\ AC=5.70\text{ cm}\)

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