Question on: SS2 Mathematics - Trigonometric Ratios II
Alice starts a \(3km\) walk from a point \(P\) on a bearing \(023{^\circ}\). She then walks \(4km\) on a bearing \(113{^\circ}\) to \(Q\). What is the distance of \(Q\) from \(P\)?
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\(\angle O = 23{^\circ} + (180{^\circ} - 113{^\circ})\)
\[\angle O = 23{^\circ} + 67{^\circ}\]
\[\angle O = 90{^\circ}\]
Using the cosine rule,
\[o^{2} = p^{2} + q^{2} - 2pq\cos O\]
\[o^{2} = 4^{2} + 3^{2} - 2(4)(3)\cos 90\]
\[o^{2} = 16 + 9 - 0\]
\[o^{2} = 25\]
\[o = \sqrt{25} = \ 5km\]
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