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Exact sine of an angle from its cosine and the exact area of a triangle from two sides

Exact sine of an angle from its cosine and the exact area of a triangle from two sides

5 marks

In triangle \(KLM\), the side \(KL\) is \(12\text{ cm}\) long and the side \(KM\) is \(5\text{ cm}\) long, as shown in the diagram.

  1. It is given that \(\cos\hat{K}=\frac{1}{4}\). Find the exact value of \(\sin\hat{K}\).[3]
  2. Hence, find the exact area of triangle \(KLM\).[2]

Solution:

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Answer:(a) \(\sin\hat{K}=\dfrac{\sqrt{15}}{4}\) (b) \(\dfrac{15\sqrt{15}}{2}\text{ cm}^2\)

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