Form 1 MathematicsA boat at point x is 200 m to the south of point Y. The boat sails X to another point Z. Point Z is 200m on a bearing of 310^{0} from X, Y and Z are on the same horizontal plane. (a) Calculate the bearing and the distance of Z from Y ( 3 marks) (b) W is the point on the path of the boat nearest to Y. Calculate the distance WY ( 2 marks) (c) A vertical tower stands at point Y. The angle of point X from the top of the tower is 6^{0} calculate the angle of elevation of the top of the tower from W (3 marks) Form 1 Mathematics
Three villages A, B and C rife Such that B is 53 km on a bearing of 295° from A and C is 75 km east of B.
(a) Using a scale of 1 cm to represent 10 km, draw a diagram to show the relative positions of villages A, B and C. (b) Determine the distance, in km, of C from A. Form 2 MathematicsA boat which travels at 5 km/h in still water is set to cross a river which flows from the north at 6km/h. The boat is set on a course of x^{0} with the north. (a) Given that cos x^{0} = ^{3}/_{5} , calculate (i) The resultant speed of the boat ( 2 marks) (ii) The angle which the track makes with the north ( 2 marks) (b) If the boat is to sail on a bearing of 135^{0}, calculate the bearing of possible course on which it can be set ( 4 marks) Form 1 Mathematics
The comer points A, B, C and D of a ranch are such that B is 8km directly East of A and C is 6km from B on a bearing of 30°. D is 7km from C on a bearing of 300°.
(a) Using a scale of 1cm to represent 1km, draw a diagram to show the positions of A, B, C and D. (b) Use the scale drawing to determine: (i) the bearing of A from D; (ii) the distance BD in kilometres. Form 1 MathematicsFor electricity posts, A,B,C, and D stand on a level ground such that B is 21 m on a bearing of 060^{0} from A, C, is 15 m to the south of B and D is 12 m on a bearing of 140^{0} from A.
Answer
Form 1 Mathematics
Points L and M are equidistant from another point K.; The bearing of L form K is 330. The bearing of M from K is 220.
Calculate the bearing of M from L Form 1 Mathematics
A plane leaves an airstrip L and flies on a bearing of 040^{0} to airstrip M, 500km away. The plane then leaves on a bearing of 316^{0} to airstrip N. The bearing ofN from L is 350^{0}. By scale drawing, determine the distance between airstrips M and N.
Form 2 MathematicsThree points O, A and B are on the same horizontal ground. Point A is 80 metres to the north of O. Point B is located 70 metres on a bearing of 060^{0} from A. A vertical mast stands at point B. The angle of elevation of the top of the mast from o is 20^{0}. Calculate: a) The distance of B from O. (2mks) b) The height of the mast in metres (2mks) Form 1 Mathematics
Three pegs R, S and T are on the vertices of a triangular plain field. R is 300 m from S on a bearing of 300° and T is 450 m directly south of R.
(a) Using a scale of 1 cm to represent 60 m, draw a diagram to show the positions of the pegs. (b) Use the scale drawing to determine: (i) the distance between T and S in metres: (ii) the bearing of T from S. (c) Find the area of the field, in hectares, correct to one decimal place. Form 1 Mathematics
Four points B,C,Q and D lie on the same plane. Point B is 42km due South – West of point Q. Point C is 50km on a bearing of S 60^{0} E from Q.
Point D is equidistant B, Q and C.
Form 1 Mathematics
Three police posts X, Y and Z are such that Y is 50 km on a bearing of 060° from X while Z is 70 km from Y and on a bearing of 300° from X.
(a) Using a suitable scale, draw a diagram to represent the above situation. (b) Determine the distance, in km, of Z from X. Form 1 Mathematics
The boundaries PQ, QR, RS and SP of a ranch are straight lines such that: Q is 16 km on a bearing of 040° from P; R is directly south of Q and east of P and S is 12 km on a bearing of 120^{0} from R.
(a) Using a scale of 1cm to represent 2 km, show the above information in a scale drawing. (b) From the scale drawing determine: (i) the distance, in kilometers, of P from S; (ii) the bearing of P from S. (c) Calculate the area of the ranch PQRS in square kilometres. Form 1 Mathematics
Three points P, Q and R are on a level ground. Q is 240 m from P on a bearing of 230^{0} . R is 120 m to the east of P
a) Using a scale of 1 cm to represent 40 m, draw a diagram to show the positions of P, Q and R in the space provided below. b) Determine i) The distance of R from Q ii) The bearing of R from Q c) A vertical post stands at P and another one at Q. A bird takes 18 seconds to fly directly from the top of the post at q to the top of the post at P. Given that the angle of depression of the top of the post at P from the top of the post at Q is 9^{0}, Calculate: i) The distance to the nearest metre, the bird covers; ii)The speed of the bird in Km/h Form 1 Mathematics
Points L and M are equidistant from another point K. The bearing of L from K is 330^{0}.
The bearing of M from K is 220^{0}.Calculate the bearing of M from L Form 1 MathematicsA helicopter is stationed at an airport H on a bearing 060^{o} and 800km from another airport P.A third airport is J is on bearing of 140^{0} and 1,200km from H. Determine:

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AuthorMaurice A Nyamoti is a Mathematics/ Computer Teacher and has passion to assist students improve grades RSS_FEED
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