(b) then, calculate the distance AC,com 196 Essential mathematics for senior secondary schools (2) 9A boat sails from port A 120 km on a bear- ing of 055° to reach port P. It then changed direction and sailed a further distance of 100 km on a bearing of 120° until it reached port B. Find: (a) the distance between port A and port B (b) the bearing of port B from port A (c) the bearing of port A from port B. 10 In the diagram below, /AB/ = 8 km, /BC/ = 13 km, the bearing of A from B is 310° and the bearing of B from C is 230°. Calculate, correct to 3 significant figures, (a) the distance AC to 2 decimal place. (WAEC 14 An aeroplane leaves an airport A and flies on a bearing 035° for 1 hours at 600 km/h to an airport B. It then flies on a bearing 130° for 1 hours direction 07 speed of the 36 km h- 18 A boat on c current of sE calculate th of the boat. 19 An aeropla Airport for of 060° for a overflying a Calculate: (a) the dist Airport road ju at 400 km/h to an airport C. Calculate the (a) distance from C to A, correct to th nearest kilometre. (b) bearing of C from A, correct to te nearest degree. 15 In the diagram, P and Q are successi (WAEC) (b) the bearing of C from A (c) how far east of B, C is. an aeroplane flyin positions of horizontally, PS and QR are vertical and R and K are points on the horizontal groun ZKSR = 41°, ZKRS = 17° and ZOKR = 21° and PS = 600 m. If th aeroplane flies from P to Q in 2 mir calculate, correct to three significant figu (a) the distance /PQ/ (b) the speed of the aeroplane in km h. (WASSCE) (b) the bea Airport 20 The town or on a bearing from Numa Sketch a di: three towns 40° (a) the dist (b) the bea P (WAEC) 11 Two boats A and B leave port P at the same 600 m time. Boat A sails 30 km in the North east direction and boat B sails 20 km on a bear- Summary ing of 300°. (a) What is the distance between the two S 1 The table b the four qua 170R boats? (b) What is the bearing of boat A from boat 21° B? 2nd que 12 A man travels from a village X on a bearing of 060° to a village Y, which is 20 km 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 dis- K 10 Two boats A and B left a port Cat the s sin 0 = +sin(! cos e = - cos time on different routes. B travelled o bearing of 150° and A travelled on North side of B. When A had travelled 8 km and B had travelled 10 k. distance between the boats was found be 12 km. Calculate the bearing of A'so tan 0 = - tan( sin is positive tance of (a) Y from Z (b) Z from X. (WAEC) 13 A man set out to travel from A to C via B. From A, he travels a distance of 8 km on a bearing N30°E to B. From B, he travels a further 6 km due east. (a) Calculate how far C is 180° 3rd quadrant sin e=-sin(0 from C. (WAEC) 17 Three towns A, B and C are situated so t AB = 60 km and AC= 100 km. The bean of B from A is 060° and the bearing of Cos 0 = -cos tan 0 = +tan(e (i) North of A; (ii) East of A, and tan is positive from A is 290°. Calculate, (a) the distance RC