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

Topical Revision Paper 12 Term 3 Unit 12: 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

(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 distance 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

(ii) BZ 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 BZ. 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