(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 (pi = frac{22}{7}), R = 6400km].Explanation
(a) < XZY = 180° – (30° + 45°) = 105°
(frac{20}{sin 105°} = frac{YZ}{sin 30°})
(YZ = frac{20 sin 30°}{sin 105°} = 10.35km)
(approxeq 10.4km ) (to 3 sig. figs)
(ii) (frac{20}{sin 75} = frac{XZ}{sin 45})
(XZ = frac{20 sin 45}{sin 75} = 14.64km)
(approxeq 14.6km) ( to 3 sig. figs)
(b) Let P and Q be two airfields.
Difference in latitude = 36° + 36° = 72°
(i) Distance between P and Q = (frac{72}{360} times 2 times frac{22}{7} times 6400)
= (frac{22}{7} times 2560)
= (8,045.71km approxeq 8,050 km) (3 sig. figs)
(ii) Time taken = (frac{8,045.71}{800} = 10.06 hours)
(approxeq 10hours) (to the nearest hour)