NJC IP4 Further Trigonometric Identities Tutorial Q2
NJC IP4 Further Trigonometric Identities Tutorial Q2
IP 4
6 marks
In the diagram, \(\triangle ABC\) and \(\triangle ACE\) are right-angled triangles. \(AC = 12\) cm, \(BC = 13\) cm, \(EC = 2AB\) and \(\angle BCE = x\) in degrees.
- Find the exact value of \(\cos x\).[4]
- Hence, show that the length of \(BD\) is \(\frac{13\sqrt{11}}{12 + \sqrt{11}}\) cm.[2]
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Answer:(i) \(\cos x=\dfrac{5(12+\sqrt{11})}{78}\) (ii) \(BD=\dfrac{13\sqrt{11}}{12+\sqrt{11}}\text{ cm}\)
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