Topical Revision Paper 12 Unit 12 Bearings Sine Cosine Rule Area of Triangle Answer

Topical Revision Paper 1 2 Term 3 Unit 1 2 : Bearings, Sine Rule, Cosine Rule and Area of Triangle Question 1: The diagram below shows the position of three locations A , B and C with respect to a reference point O . The bearings of A , B and C from O are 050 , 135 and 240 respectively. It is also given that 120OA m and 150OB m. (i) Find the bearing of B from A . [2] (ii) If the bearing of B from C is 100 , calculate the length of OC . [2] (iii) A mast stands vertically at B such that the angle of elevation of the top of the mast from O is 62 . Find the height of the mast. [2] Answer: (i) 175.6 (ii) 133.8OC  m (iii) height 282.1 m Question 2: In the diagram A , B and S represent three points in the sea. B is 3 km from A on a bearing of 060 . The bearings of S from A and B are 110 and 155 respectively. B A C O N 50 120 150 175.6 deg 133.8m 282.1m

(i) Calculate the distance AS . [2] (ii) A ship at S sails directly to A at a steady speed of 2 1kmh . After 40 minutes, the ship is at T, a point on AS. (a) Calculate the d istance BT . [3] (b) Find the bearing of B from T . [2] (iii) A hot air balloon, H , is lowering at a point 600 m vertically above B . Calculate the greatest angle of elevation of H from an observer on the ship as the ship sails from S to A . [2] Answer : (i) 4.23AS km (ii) (a) 2.49BT km (b) 0357.3 (iii) 014.6 Question 3: The diagram shows three points, A , B and C on a piece of horizontal land. It is given that AB = 400 m, BC = 330 m, AC = 710 m and B is due North of A . (i) Calculate (a ) ABC , [2] (b ) the area of triangle ABC , [2] (c ) the bearing of C from A . [2] North B C A 710 m 330 m 400 m 4.23km 2.49km 357.3 deg 14.6 deg 153.0 deg 30,000 m2 12.2 deg

(ii) B Z is a tower crane standing vertically at B and the angle of elevation of Z from A is 18 . Calculate the height of the tower crane. [2] (iii) A car moves along the path AC until it reaches a point P which is nearest to the tower crane B Z . Calculate the largest angle of depression of the point P from Z . [2] Answer : (i) (a) 153.0ABC   (b) 230000 m (c) Bearing is 012.2 (ii) 130 mBZ  (iii) 57.0 Question 4: A man, at point M , is 80 metres at a bearing of 200 from an observation deck, D , which stands 25 metres tall. He begins to walk to a point P which is due East of D at a bearing of 050 . Ignoring the man’s height, calculate (i) the angle of elevation of the top of the deck from the man at M , [2] (ii) the distance he walks when the angle of elevation of the top of the deck from his position is the greatest, and [2] (iii) the distance DP . [2] Answer: (i) 17.4 (ii) 62.2 mDP (iii) 69.3 m M North East D P 200 North 50 130m 57.0 deg 17.4 deg 62.2 m 40sqrt(3) or 69.3m