20 original questions, 65 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.
Write down the name of the side that is the hypotenuse.
Show that the three lengths fit Pythagoras' theorem.
2 marks
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a) PRb) 5² + 12² = 25 + 144 = 169 and 13² = 169
2
Triangle ABC is a right-angled triangle with the right angle at B.
AB = 6 cm and BC = 8 cm.
Work out the length of AC.
2 marks
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10 cm
3
Triangle PQR is a right-angled triangle with the right angle at Q.
PQ = 7 cm and QR = 9 cm.
Work out the length of PR.
Give your answer correct to 1 decimal place.
2 marks
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11.4 cm
4
The diagram shows a right-angled triangle.
Work out the length x.
2 marks
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7.5 cm
5
The diagrams show two right-angled triangles.
Work out the length x.
Work out the length y. Give your answer correct to 1 decimal place.
3 marks
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a) 15 cmb) 9.7 cm
6
A rectangle is 9 cm long and 6 cm wide.
Work out the length of a diagonal of the rectangle.
Give your answer correct to 1 decimal place.
2 marks
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10.8 cm
7
A is the point (1, 2) and B is the point (7, 10). Work out the length of the line segment AB.
C is the point (−3, 4) and D is the point (2, −8). Work out the length of the line segment CD.
3 marks
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a) 10b) 13
8
A triangle has sides of length 10 cm, 24 cm and 26 cm.
Show that the triangle is a right-angled triangle.
3 marks
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102 + 242 = 100 + 576 = 676 = 262, so by the converse of Pythagoras' theorem the triangle is right-angled
9
A rectangular football pitch is 100 m long and 64 m wide.
Sam runs from one corner to the opposite corner along the diagonal. Tom runs from the same corner to the same opposite corner along two sides of the pitch.
How much further does Tom run than Sam? Give your answer correct to 1 decimal place.
3 marks
Show answer
45.3 m
10
ABCD is a trapezium in which AB is parallel to DC.
Angle ADC = angle DAB = 90°.
AB = 9 cm, AD = 12 cm and DC = 14 cm.
Work out the perimeter of the trapezium.
4 marks
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48 cm
11
The diagram shows an isosceles triangle with two sides of 13 cm and a base of 10 cm.
Work out the perpendicular height h of the triangle.
Work out the area of the triangle.
4 marks
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a) 12 cmb) 60 cm²
12
A field ABCD is a trapezium in which AB is parallel to DC.
Angle DAB = angle ADC = 90°.
AB = 25 m, AD = 15 m and DC = 33 m.
Joe wants to put a fence around the whole perimeter of the field.
Fencing is sold in 12 m rolls. Each roll costs £19.50.
Work out the total cost of the rolls of fencing Joe must buy.
5 marks
Show answer
£156
Extension questions: beyond the core Year 9 objectives, for pupils who want a stretch.
13
ABC is a right-angled triangle. AB = 12 cm, BC = 5 cm and AC = 13 cm. Angle BAC = θ
Write down which side is the hypotenuse, which side is opposite θ and which side is adjacent to θ
Write sin θ, cos θ and tan θ as fractions.
4 marks
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a) hypotenuse AC, opposite BC, adjacent ABb) sin θ = 5/13, cos θ = 12/13, tan θ = 5/12
14
Work out the length of the side marked with a letter in each triangle. Give each answer correct to 3 significant figures.
4 marks
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a) 9.64 cmb) 16.4 cmc) 11.2 cm
15
Work out the size of the angle marked a, b and c. Give each answer correct to 1 decimal place.
4 marks
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a) 35.7°b) 50.0°c) 61.4°
16
A wheelchair ramp is 4.5 m long. It makes an angle of 8° with the horizontal ground.
Work out the height, h, that the ramp rises. Give your answer correct to 3 significant figures.
Work out the horizontal distance, d, that the ramp covers. Give your answer correct to 3 significant figures.
A safety rule says a ramp should rise no more than 1 m for every 12 m across. Does this ramp follow the rule? Show how you decide.
4 marks
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a) 0.626 mb) 4.46 mc) No: 0.626 ÷ 4.46 × 12 = 1.69 m, more than 1 m
17
Sofia stands 25 m from the foot of a tree, on level ground. The angle of elevation of the top of the tree from where she stands is 32°. Work out the height of the tree, h. Give your answer correct to 3 significant figures.
The top of a cliff is 60 m above the sea. From the top of the cliff, the angle of depression of a boat is 18°. Work out the distance, d, of the boat from the foot of the cliff. Give your answer correct to 3 significant figures.
4 marks
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a) 15.6 mb) 185 m
18
In triangle ABC, angle ABC = 90° and angle BAC = 30°.
AC = 14 cm.
Without using a calculator, work out the length of BC.
You must show your working.
3 marks
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7 cm
19
In triangle ABC, angle BAC = 35°, angle ABC = 78° and BC = 9.4 cm.
Work out the length of AC. Give your answer correct to 3 significant figures.
3 marks
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16.0 cm
20
In triangle ABC, AB = 8 cm, AC = 11 cm and angle BAC = 62°.
Work out the length of BC. Give your answer correct to 3 significant figures.
4 marks
Show answer
10.1 cm
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Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.