Math homework help
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Show all your workings clearly.
1. Two ships are observed from point O.
At a particular time their positions A and B are
as shown on the right.
The distance between the ships at this time is
A. 3.0 km
B. 3.2 km
C. 4.5 km
D. 9.7 km
E. 10.4 km
[VCAA 2005 Further Maths Exam 1]
2. The bearing of an aeroplane, X, from a control tower, T, is 055°. Another aeroplane, Y, is due east of control tower T. The bearing of aeroplane X from aeroplane Y is 302°.
The size of the angle TXY is
[VCAA 2005 Further Maths Exam 1]
A. 32°
B. 35°
C. 55°
D. 58°
E. 113°
A
B
C
4 km
6 km
N
3. A hiker walks 4 km from A on a bearing of 30º to a point B,
then 6 km on a bearing of 330º to a point C. The distance AC
in km is
D 6 sin 60º
4. Ship A and Ship B can both be seen from the lighthouse. Ship A is 5 km from the lighthouse,
on a bearing of 028o. Ship B is 5 km from Ship A, on a bearing of 130o.
(a) Two angles, x and y, are shown in the diagram.
(i) Determine the size of the angle x in degrees.
(ii) Determine the size of the angle y in degrees.
(b) Determine the bearing of the lighthouse from
Ship A.
(c) Determine the bearing of the lighthouse from
Ship B.
5. Starting from the camp at C, Tim takes a bearing of a mountain at M and notes it to be 25°.
He then walks 5 km to the hut at H and takes a second bearingof the same mountain and it is 345°.
(a) Work out the angles in the triangle CHM. Prove that it is a right angled triangle.
(b) From the mountain at M:
(i) what is the bearing of the camp? (ii) what is the bearing of the hut?
(c) How far is it (i) from the camp to the mountain (ii) from the hut to the mountain?
(d) Tim walks back to camp from the hut. What bearing does he follow?
6. The base of a lighthouse D, is at the top of a cliff 168 metres above sea level. The angle of depression from D to a boat at C is 28o. The boat heads towards the base of the cliff, A, and stops at B. The distance AB is 128 metres.
(a) What is the angle of depression from D to B, correct to the nearest minute?
(b) How far did the boat travel from C to B, correct to the nearest metre?
7. Genie Construction is building a new shopping plaza on a plot of land that is a trapezium with the two parallel sides pointing north. The following is a diagram, which is not drawn to scale, of the plot:
160 m
230 m
Part 1
(a) Find the area and the perimeter of the site ABCD.
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