The Robert Smyth School Y11 Topic 15
Mathematics Faculty Trig 2
Bearings
1. The diagram shows the positions of three towns, P, Q and R.
Q is 35 km from P on a bearing 100°.
R is 42 km from P on a bearing 120°.
Calculate the distance from Q to R.
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Answer...... km
(Total 4 marks)
2. Two ships, A and B, leave a port at 1300 hours. Ship A travels at a constant speed of 18 km per hour on a bearing of 070°. Ship B travels at a constant speed of 25 km per hour on a bearing of 152°.
Calculate the distance between A and B at 1400 hours.
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Answer ...... km
(Total 4 marks)
Sine and Cosine Rule
1. In the diagram, PQ = 14 cm and QR = 8.6 cm.
Angle PSQ = angle SQR = 90°
Angle PQS = 25°
Calculate angle R.
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Answer ...... degrees
(Total 5 marks)
2. In triangle ABC, AB = 11 cm, BC = 9 cm and CA = 10 cm.
Find the area of triangle ABC.
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Answer ...... cm2
(Total 5 marks)
3. (a) ABC is a triangle.
AC = 19 cm, BC = 17 cm and angle BAC = 60°
Calculate the size of angle ABC.
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Answer ...... degrees
(3)
(b) PQR is a triangle.
PR = 23 cm, PQ = 22 cm and angle QPR = 48º
Calculate the length of QR.
Give your answer to an appropriate degree of accuracy.
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Answer ...... cm
(4)
(Total 7 marks)
4. The hour hand of a clock is 4.5 cm long.
The minute hand is 6.2 cm long.
Calculate the distance between the tips of the hands at 7 o’clock.
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Answer ...... cm
(Total 4 marks)
5. ABCD is a quadrilateral.
AB = 7 cm, AD = 6 cm and BC = 9 cm.
Angle ABC = 75° and angle ADC = 90°
Calculate the perimeter of ABCD.
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Answer ...... cm
(Total 5 marks)
6. In triangle ABC, AB = 5 cm, BC = 8 cm and AC = 9 cm.
Use the cosine rule to show that triangle ABC does not contain an obtuse angle.
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(Total 3 marks)
7. A shape is made from 6 congruent triangles as shown.
You are given that sin 30° = 0.5
Calculate the area of the shape.
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Answer ………………………………………………
(Total 4 marks)
Similar Triangles
1. The triangles A and B are congruent.
(a) Write down the values of x and y.
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Answer x =...... cm, y = ………………… cm
(2)
(b) Given that sin 30° = 0.5, calculate the area of triangle A.
State the units of your answer.
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Answer ......
(3)
(Total 5 marks)
2. Triangles ADE and ABC are similar.
DE is parallel to BC.
AD = 4 cm, DE = 6 cm and BC = 9 cm.
Calculate the length of BD.
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Answer ...... cm
(Total 3 marks)
3. Triangles ABC and PQR are similar.
AC = 3.2 cm, AB = 4 cm and PR = 4.8 cm.
(a) Explain why sin x = 0.8
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(1)
(b) Calculate the length of PQ.
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Answer ...... cm
(3)
(Total 4 marks)
4. Triangles ABC and APQ are similar.
PQ is parallel to BC.
AQ = 6 cm, QC = 2 cm and BC = 12 cm
Calculate the length of PQ.
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Answer...... cm
(Total 3 marks)
5. A square-based pyramid A is divided into two parts:
a square-based pyramid B and a frustum C, as shown.
Pyramid A is similar to pyramid B.
The base of pyramid A is a square of side 10 cm. The base of pyramid B is a square of side 5 cm.
The vertical height of pyramid A is 12 cm.
(a) You are given the formula
Volume of a pyramid = area of base × vertical height
Calculate the volume of the frustum C.
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Answer ...... cm3
(4)
(b) Express the volume of the frustum C as a fraction of the volume of the larger pyramid A. Give your answer in its simplest form.
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Answer ......
(2) (Total 6 marks)
Trig Graphs
1. (a) Sketch the graph of y = sin x for values of x from 0° to 360°.
(1)
(b) One solution of the equation sin x = 0.92 is x = 67°.
Use your sketch graph to find another solution of this equation.
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Answer ...... degrees
(2)
(c) Use your sketch graph to work out the value of sin 293°.
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Answer ......
(1)
(Total 4 marks)
2. The sketch shows the graph of y = sin x for 0° £ x £ 360°
You are given that sin 70° = 0.9397
(a) Write down another solution of the equation sin x = 0.9397
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Answer ...... degrees
(1)
(b) Solve the equation sin x = –0.9397 for 0° £ x £ 360°
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Answer ...... degrees
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(2)
(c) On the axes below sketch the graph of y = sin 2x for 0° £ x £ 360°
(2)
(d) Hence write down the four solutions of the equation sin 2x = 0.9397
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Answer ...... degrees
...... degrees
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...... degrees
(3)
(Total 8 marks)
The Robert Smyth School 3