Paper 2 June 2023 Foundation tier, Question 22 3 marks
The diagram shows a right-angled triangle.
Work out the value of a.
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Topic questions Pure mathematics Exact trigonometric values
Exact trigonometric values
12 questions · 66 marks · about 1 hour
Exact trigonometric values questions
TopicExact trigonometric values▾
OCR J560 Exact trigonometric values 12 questions
Paper 5 June 2023 Higher tier, Question 13 6 marks
The diagram shows a triangle, ABC, with perpendicular height BD.
BC = 12 cm, angle BCD = 30° and angle BAD = 45°.
(a)
[3]
Work out the length of BD.
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(b)
[3]
Work out the exact length of AB. Give your answer in its simplest form.
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Paper 5 November 2022 Higher tier, Question 17 3 marks
The diagram shows triangle ABC.
Find the area of the triangle.
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Paper 2 June 2022 Foundation tier, Question 19 3 marks
(a)
[1]
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(b)
[2]
Here is a right-angled triangle.
Work out the value of x.
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Paper 5 June 2022 Higher tier, Question 15 4 marks
Also involves Surds
ABC is an equilateral triangle of side length 2 cm. M is the midpoint of AC.
Using this diagram, show that tan 30° = 
.
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Paper 5 November 2021 Higher tier, Question 11 7 marks
The diagram shows a quadrilateral ABCD.
AD = 10 cm, angle BAD = 30° and angle ABD = angle BDC = 90°.
The ratio of length BD to length DC is 1: 2.4.
Work out length BC. You must show your working.
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Paper 5 November 2019 Higher tier, Question 19 7 marks
(a)
[1]
Write down the value of sin 45°.
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(b)
[6]
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Paper 5 November 2018 Higher tier, Question 13 8 marks
In the diagram, ABC is a right-angled triangle. P is a point on AB. BC = 40 m, AP = 20 m and angle ABC = 30 °.
(a)
[3]
Show that AC = 20 m.
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(b)
[5]
Find the length of PB.
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Paper 5 June 2018 Higher tier, Question 11 6 marks
The diagram shows two right-angled triangles ABD and BCD, sharing a common side BD. AD = 10 cm, BC = 12 cm and angle DBC = 60°.
Work out the length of AB.
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Paper 2 November 2017 Foundation tier, Question 19, also on the Higher paper 6 marks
Also involves Trigonometric ratios
The angles in a triangle are in the ratio 1: 2: 3.
(a)
[2]
Show that the triangle is a right-angled triangle.
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(b)
[4]
The hypotenuse of the triangle is 15 cm long.
Calculate the length of the shortest side in the triangle.
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Paper 5 November 2017 Higher tier, Question 8, also on the Foundation paper 6 marks
The angles in a triangle are in the ratio 1: 2: 3.
(a)
[2]
Show that the triangle is a right-angled triangle.
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(b)
[4]
The hypotenuse of the triangle is 15 cm long.
Calculate the length of the shortest side in the triangle.
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Paper 5 June 2017 Higher tier, Question 20 7 marks
The diagram shows some land in the shape of a quadrilateral, ABCD.
AB = 3 km, AD = 5 km, CD = 12 km and angle BAC = 30°.
The land is sold for £10 million per square kilometre.
Calculate the total cost of the land.
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