Exact cosine of the sum of two angles at the apex of a triangle divided by an altitude
Exact cosine of the sum of two angles at the apex of a triangle divided by an altitude
IB Year 6 | Grade 12
5 marks
In the diagram, \(S\) is the point on \(QR\) such that \(PS\) is perpendicular to \(QR\). It is given that \(QS=3\), \(SR=2\) and \(PS=4\). The angles \(QPS\) and \(SPR\) are \(\alpha\) and \(\beta\) respectively.
Without using a calculator, find the exact value of \(\cos(\alpha+\beta)\).[5]
Solution:
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Answer:\(\dfrac{\sqrt5}{5}\)
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