Exact tangent and cosine in a right-angled triangle whose squared sides are terms of an arithmetic progression
Exact tangent and cosine in a right-angled triangle whose squared sides are terms of an arithmetic progression
IB Year 6 | Grade 12
5 marks
In triangle \(ABC\), \(\angle ACB=90^\circ\), \(BC=a\), \(CA=b\) and \(AB=c\). The numbers \(a^2\), \(b^2\) and \(c^2\) are, in that order, the first, second and fourth terms of an arithmetic progression. Determine \(\tan A\) and \(\cos A\), giving each as an exact value.[5]
Solution:
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Answer:\(\tan A=\frac{\sqrt6}{3}\), \(\cos A=\frac{\sqrt{15}}{5}\)
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