Trigonometry and Circular measurement

Calculate the lengths marked with letters. All lengths are in cm. Give answers correct to 3 significant figures.

3.35cm
3.01cm
4.65cm
4.24cm

Calculate the lengths marked with letters. All lengths are in cm. Give answers correct to 3 significant figures.

5.35cm
4.25cm
3.75cm
4.95cm

Find the lengths marked with letters. All dimensions are in cm.

25.5cm
15cm
17.6cm
12.25cm

Calculate the lengths marked with letters. All lengths are in cm. Give answers correct to 3 significant figures.

x = 5.56cm, y = 6.4cm
x = 7.5cm, y = 12.4cm
x = 8.75cm, y = 10.4cm
x = 7.71cm, y = 16.4cm

Calculate the lengths marked with letters. All lengths are in cm. Give answers correct to 3 significant figures.

x = 21.4cm
x = 19.5cm
12.94cm
6.5cm

Calculate the lengths marked with letters. All lengths are in cm. Give answers correct to 3 significant figures.

21cm
16.5cm
17.6cm
5.6cm

Calculate the lengths marked with letters. All lengths are in cm. Give answers correct to 3 significant figures.

255cm
295cm
125cm
312cm

Find the angles marked with letters. Give answers correct to 1 decimal place.

41.3°
43.5°
56°
49.5°

A crank-connecting rod mechanism is shown below. Calculate, for the position shown, the distance AC and angle BAC.

AC = 2.29m, angle BAC = 65°
AC = 1.0m, angle BAC = 65.5°
AC = 1.29m, angle BAC = 76.5°
AC = 1.9m, angle BAC = 75°

A tie wire 6.0m long is fixed at one end to the top of a vertical radio mast 4.2 m tall, and the other end is bolted to the horizontal ground. Calculate the angle of inclination of the wire from the ground and the distance of the bolted joint from the foot of the mast.

4.25°, 5.3m
44.4°, 4.28m
24.4°, 42m
54.5°, 4.65m

In this vector diagram, calculate the voltage V_R across the resistance and the phase angle Φ.

VR = 115V, Φ = 35.4°
VR = 110V, Φ = 55.4°
VR = 105V, Φ = 45.4°
VR = 95V, Φ = 65.4°

Determine all unspecified angles and side lengths in the triangle ABC shown in figure below.

angle ABO = angle OCB = 47°, angle OBC = 33°
angle ABO = angle OCB = 57°, angle OBC = 53°
angle ABO = angle OCB = 17°, angle OBC = 44°
angle ABO = angle OCB = 27°, angle OBC = 63°

A boy is flying a kite from a string of length 60m. If the string is taut and makes an angle of 71° with the horizontal, what is the height of the kite? Ignore the height of the boy.

56.73m
67.63m
43.36m
62.25m

The frame of a bicycle is shown in the diagram. Find the length of the cross bar.

90.55cm
90.66cm
90.33cm
90.28cm

AB and PQ are two straight lines supporting a vertical pole on horizontal ground.

(a) A is 7m from F, foot of the pole. The length of the wire AB is 8m. Calculate the angle BAF

(b) The length of the wire PQ is 5m and the angle PQG = 54°. Calculate PG, the height of P above the ground

(c) The width of the pole FG is 0.35m. Calculate the distance between A and Q

(a) 29° (b) 4.05m (c) 10.3m
(a) 35° (b) 5.5m (c) 8.25m
(a) 25° (b) 8.05m (c) 15.1m
(a) 25° (b) 25.05m (c) 25.3m

Convert the following to radians leaving the answer as a multiple of π:

120°

\[{2 π\over 3}\]
\[{4 π\over 3}\]
\[{4 π\over 4}\]
\[{6 π\over 3}\]

Convert the following to radians leaving the answer correct to 2 decimal places:

223.92°

1.95 rad
3.91 rad
2.42 rad
3.55 rad

Convert the following radians to degrees giving your answer to the nearest degree:

7π/12

15°
150°
125°
105°

Find the length of the arc of a circle of radius 5.5cm when the angle subtended at the centre is 1.20 radians.

3.65cm
6.60cm
3.55cm
4.22cm

Determine the shaded area in the figure below.

\[{396mm^2}\]
\[{300mm^2}\]
\[{296mm^2}\]
\[{345mm^2}\]

Trigonometry and Circular measurement

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1. Question

2. Question

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9. Question

A crank-connecting rod mechanism is shown below. Calculate, for the position shown, the distance AC and angle BAC.

10. Question

11. Question

12. Question

13. Question

14. Question

15. Question

AB and PQ are two straight lines supporting a vertical pole on horizontal ground.

(a) A is 7m from F, foot of the pole. The length of the wire AB is 8m. Calculate the angle BAF

(b) The length of the wire PQ is 5m and the angle PQG = 54°. Calculate PG, the height of P above the ground

(c) The width of the pole FG is 0.35m. Calculate the distance between A and Q

16. Question

17. Question

18. Question

19. Question

20. Question

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