GATE 2024 CE (CE2) – Question 64
A child walks on a level surface from point P to point Q at a bearing of 30°, from point Q to point R at a bearing of 90° and then directly returns to the starting point P at a bearing of 240°. The straight-line paths PQ and QR are 4 m each. Assuming that all bearings are measured from the magnetic north in degrees, the straight-line path length RP (in meters) is _________________ (rounded off to the nearest integer).
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Correct answer: 7
Explanation
Take P as the origin with the x-axis to the east and the y-axis to the north. Then $Q = (4\sin 30°, 4\cos 30°) = (2, 3.464)$ and, with QR going due east, $R = (6, 3.464)$. The distance $RP = \sqrt{6^2 + 3.464^2} = \sqrt{48} = 6.93 \approx 7$ m. (The bearing of RP is $180° + \tan^{-1}\frac{6}{3.464} = 240°$, as stated.)