trigonometry revision exercise

8/6/2019 Trigonometry Revision Exercise

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Trigonometry

Revision ExerciseWritten by: CWW

1. On the diagram, AB = 8 cm, BC= 6 cm, and CBA

= 90.

Calculate

(i) AC

(ii) sin BCA

, expressing your answer in fraction.

(iii) cos DAC

, expressing your answer in fraction.

2. On the diagram below shows a right-angled triangle.

Given that cos DCA

=25

24 , calculate

(i) AC

(ii) AB(iii) sin CAB , expressing your answer in fraction.

(units is in cm)

3. On each of the following diagrams, calculate the unknowns (units in cm).

(a) (b)

(c) (d)

4. On each of the following diagrams, calculate the unknown (units in cm).


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(a) (b) (c)

(d) (e) (f)

5. For the following diagrams, calculate its area in cm.

(a) (b)

(c) (d)

6. A girl, G, sitting down and look at the bird, B, flying above point A. The distance

between point A and the girl is 10 m and the angle of elevation of the bird from the

girl is 38. Calculate the height between the bird and point A.

7. A boy sits on the edge of a cliff and look downwards to see a boat. The height of

the cliff is 70 m and the distance between the foot of the cliff to the boat is 150 m.

Calculate the angle of depression of the boat as seen from the boy.

8. A man, 1.7 m tall, is viewing the top of a tree, which is 12 m away from him. The

angle of elevation of the top of the tree when viewed by the man is 30. Calculate

the height of the tree.

9. A and B are two viewing points on the ground in front of a hill. The distance


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between the two points is 100 m. The angle of elevation of the top of the hill when

viewed from point A and pointB are 35 and 46 respectively. Calculate the height

of the hill.

10. A, B and Care three points on the ground and lies on the same line. The distance

between A and B is 150 m. There is a hot air balloon hovering directly above C.

The angle of elevation of the hot air balloon when viewed from A and B are 30

and 45 respectively. Calculate the distance between the hot air balloon and point

C.

11. In the diagram, a flag pole, BC, is standing at C, and there is a slope in front of it.

It is given that the distance from A to D is 120 m, DAC

= 20 and CAB =

22.

Calculate the height of the flag pole, BC.

12. A, B and Care three points on the horizontal field. Cis due east ofA.

(a)Given that AB = 76 m, BC= 81 m and CBA

= 110, calculate

(i) AC

(ii) CAB

(iii) the bearing ofB from A

(iv) the bearing ofA from B

(v) the bearing ofB from C.

(b) A white doveD is flying directly above B at an altitude of 30 m. Calculate

(i) the angle of elevation of the dove viewed from C; and

(ii) the greatest angle of elevation of the dove viewed fromAC.


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13. A, B and Care three different ports on the horizontal field. B is directly south of

C.

(a) Given that CBA

is 102, AB = 125 km and BC= 60 km, calculate

(i) the bearing ofA from B,

(ii) AC

(iii) CAB(iv) the bearing ofCfrom A.

(c) A cargo ship is travelling at a speed of 40 km/h from portA to port Cthrough

the route AC. Given that the cargo ship leave port A at 12 45, calculate(i) the time it reached C.

(ii) the distance travelled by the cargo ship such that it is nearest to portB.

14. On the diagram shows a solid made up of a cuboid and a pyramid.

(a) Given thatAB = 24 cm, BC= 18 cm, AE= 7 cm, calculate

(i) AC

(ii) CH

(iii) BG

(iv) DGB

(b) Given that the midpoint ofACand BD is K, and the midpoint ofEG and FHis

J, calculate(i) KBA

(ii) CJK

(c) Given that KI= 11 cm, calculate

(i) IJ

(ii) FIG

(d) Calculate the volume of the solid.

15. For each of the question, find x where 1800 x .

(a) cos x = 0.731 (d

)

sin x = 0.652

(b)

tan x = 1.48 (e) cos x = 0.719


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(c) sin x = 0.866 (f) tan x = 0.918

ANSWER KEY

1 (i) 10 cm 11 64.4 m

(ii)5

4 12 (a) (i) 129 m(ii) 36.3

(iii)

5

4

(iii) 053.7

(iv) 233.7

2 (i) 25 cm (v) 303.7

(ii) 7 cm (b) (i) 20.3

(iii)

25

24 (ii) 33.7

13 (a) (i) 258

3 (a) 36.9 (ii) 149 km

(b) 15.9 cm (iii) 23.1

(c) 23.9 cm (iv) 054.9(d) 21.5 cm (b) (i) 16 29

4 (a) 33.6 cm (ii) 115 km

(b) 31.3 cm 14 (a) (i) 30 cm

(c) 74.7 (ii) 25 cm

(d) 80.8 cm (iii) 19.3 cm

(e) 28.4 (iv) 84.2

(f) x = 45.8

y = 53.8

(b) (i) 51.3

(ii) 65.0

5 (a) 695 cm (c) (i) 4 cm

(b) 112 cm (ii) 70.9

(c) 4920 cm (d) 3600 cm(d) 67.3 cm 15 (a) 43.0

6 7.81 m (b) 56.0

7 25.0 (c) 60.0, 120.0

8 8.63 m (d) 40.7, 139.3

9 216 m (e) 136.0

10 205 m (f) 137.4

trigonometry revision exercise

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