Theory question 110
Bearings(a) A man travels from a village X on a bearing of 060° to a village Y which is 20km away. From Y, he travels to a village Z, on a bearing of 195°. If Z is directly east of X, calculate, correct to three significant figures, the distance of: (i) Y from Z (ii) Z from X.
(b) An aircraft flies due south from an airfield on latitude 36°N longitude 138°E to an airfield on latitude 36°S longitude 138°E. (i) Calculate the distance travelled, correct to three significant figures (ii) if the speed of the aircraft is 800km per hour, calculate the time taken, correct to the nearest hour. [Take π = 22/7 R = 6400km].
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(a) ∠YXZ = 90° − 60° = 30°; ∠XYZ = 240° − 195° = 45°; ∠XZY = 105°
(i) YZ = 20 sin 30°/sin 105° = 10/0.9659 ≈ 10.4 km
(ii) XZ = 20 sin 45°/sin 105° = 14.14/0.9659 ≈ 14.6 km
(b)(i) Angle between the latitudes = 36° + 36° = 72° along a meridian (a great circle)
Distance = 72/360 × 2 × 22/7 × 6400 ≈ 8046 km ≈ 8050 km
(ii) Time = 8046 ÷ 800 ≈ 10 hours
Draw north lines at X and Y to find the angles of the triangle, then use the sine rule.