Question
The diagram shows the positions of three points A, B and C in a field.
(a) Show that BC is 118.1m, correct to 1 decimal place.
(b) Calculate angle ABC.
Angle ABC = …………………………………………
(c) The bearing of C from A is 147°.
Find the bearing of
(i) A from B,
………………………………………….
(ii) B from C.
………………………………………….
(d) Mitchell takes 35 seconds to run from A to C.
Calculate his average running speed in kilometres per hour.
…………………………………. km/h
(e) Calculate the shortest distance from point B to AC.
……………………………………… m
Answer/Explanation
(a)\( BC^{2}=80^{2}+115^{2}-2\times 80\times 115\cos 72\)
118.06…
(b) 67.8 or 67.9 or 67.83 to 67.88
(c)(i) 255
(c)(ii) [00]7.2
(d) 11.8 or 11.82 to 11.83
(e) 76.1 or 76.08 to 76.09
Question
The diagram shows a field, ABCD, on horizontal ground.
BC = 192m, CD = 287.9m, BD = 168m and AD = 205.8m.
(a) (i) Calculate angle CBD and show that it rounds to 106.0°, correct to 1 decimal place.
(ii) The bearing of D from B is 038°.
Find the bearing of C from B.
………………………………………….
(iii) A is due east of B.
Calculate the bearing of D from A.
………………………………………….
(b) (i) Calculate the area of triangle BCD.
……………………………………..\( m^{2}\)
(ii) Tomas buys the triangular part of the field, BCD.
The cost is \($35 750\) per hectare.
Calculate the amount he pays.
Give your answer correct to the nearest \($100.\)
[1 hectare = \(10000m^{2}\)]
\($ …………………………………………\)
Answer/Explanation
(a)(i) 106.01 to 106.02
(ii) 292.0 or 291.98 to 291.99
(iii) 310.0 or 310.03 to 310.04
(b)(i) 15 500 or 15 501 to 15 503. …
(ii) 55 400
Question
The diagram shows a field ABCDE.
(a) Calculate the perimeter of the field ABCDE.
m [4]
(b) Calculate angle ABD.
Angle ABD = [4]
(c) (i) Calculate angle CBD.
Angle CBD = [2]
(ii) The point C is due north of the point B.
Find the bearing of D from B.[2]
(d) Calculate the area of the field ABCDE.
Give your answer in hectares.
[1 hectare = 10 000m2]
hectares [4]
Answer/Explanation
Ans:
3(a) 530
3(b) 52.9 or 52.89…
3(c)(i) 28.1 or 28.07…
3(c)(ii) 331.9 or 331.9…
3(d) 1.5[0] or 1.498… nfww