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.
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.
A plane leaves an airstrip L and flies on a bearing of 0400 to airstrip M, 500km away. The plane then leaves on a bearing of 3160 to airstrip N. The bearing ofN from L is 3500. By scale drawing, determine the distance between airstrips M and N.
Three 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 0600 from A. A vertical mast stands at point B. The angle of elevation of the top of the mast from o is 200.
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.
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.
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 1200 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.
Three points P, Q and R are on a level ground. Q is 240 m from P on a bearing of 2300 . 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 90, Calculate:
i) The distance to the nearest metre, the bird covers;
ii)The speed of the bird in Km/h
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