Theory question 111
Bearings(a) Triangle PQR is right-angled at Q, PQ = 3a cm and QR = 4a cm. Determine PR in terms of a. (b) Ayo travels a distance of 24km from X on a bearing of 60° to Y. He then travels a distance of 18km to a point Z and Z is 30km from X. (i) Draw the diagram to show the positions of X, Y and Z (ii) What is the bearing of Z from Y? (iii) Calculate the bearing of X from Z.
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(a) PR2 = (3a)2 + (4a)2 = 25a2 ⇒ PR = 5a cm.
(b)(i) Sketch X, Y on bearing 060° from X (24 km), Z 18 km from Y, XZ = 30 km.
Since 242 + 182 = 900 = 302, ∠XYZ = 90°.
(ii) Bearing of X from Y = 240°; YZ is perpendicular to YX, so the bearing of Z from Y = 240° − 90° = 150°.
(iii) tan ∠YZX = 24/18 ⇒ ∠YZX = 53.1°. Bearing of Y from Z = 330°, so the bearing of X from Z = 330° − 53.1° = 276.9° ≈ 277°.
Check for a 3-4-5 triangle before using the cosine rule.