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"Full Coverage": Trigonometry of Right-Angled Triangles

This worksheet is designed to cover one question of each type seen in past papers, for each GCSE Higher Tier topic. This worksheet was automatically generated by the DrFrostMaths Homework Platform: students can practice this set of questions interactively by going to www.drfrostmaths.com/homework, logging on, Practise → Past Papers/Worksheets (or Library → Past/Past Papers for teachers), and using the ‘Revision’ tab.

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Question 1
Categorisation: Determine one of the shorter sides of a right-angled triangle.

[Edexcel IGCSE June2010-3H Q7] Work out the value of 𝑥 .

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Question 2
Categorisation: As above (but using a different trigonometric ratio).

[Edexcel IGCSE June2011-4H Q11] Calculate the length of LM. Give your answer correct to 3 significant figures.

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Question 3
Categorisation: As above (again using a different trigonometric ratio, and with the triangle in a different orientation)

[Edexcel IGCSE May2012-4H Q6] Calculate the length of MN.

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Question 4
Categorisation: Determine the hypotenuse of a right-angled triangle.

[AQA IGCSE FM June2012-P2 Q10]
An aircraft flies 𝑦 kilometres in a straight line at an angle of elevation of 28°
The gain in height is 7 kilometres. Work out the value of 𝑦 .

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Question 5
Categorisation: Use trigonometry twice, where one triangle is embedded in another.
[Edexcel IGCSE June2011-3H Q18] Triangle ABC is right-angled at B. Angle BAC = 32° AC = 47 m.
D is the point on AB such that angle BDC = 51°

Calculate the length of BD. Give your answer correct to 3 significant figures.

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Question 6
Categorisation: As above, but for non-embedded triangles.
[Edexcel IGCSE Jan2016-4H Q19] 𝑃𝑆𝑅 is a straight line.
Angle 𝑃𝑆𝑄 = 90°   𝑃𝑆 = 8.4 cm    Angle 𝑄𝑃𝑆 = 38°   Angle 𝑆𝑄𝑅 = 44°
Work out the length of 𝑄𝑅. Give your answer correct to 3 significant figures.

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Question 7
Categorisation: Use a combination of Pythagoras’ theorem and trigonometry.

[Edexcel GCSE June2012-2H Q18]
The diagram shows a quadrilateral ABCD. AB = 16 cm. AD = 12 cm. Angle BCD = 40°
Angle ADB = angle CBD = 90°
Calculate the length of CD. Give your answer correct to 3 significant figures.

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Question 8
Categorisation: Determine a distance in a 3D diagram using trigonometry, and
under that ‘angle of elevation’ is the angle upwards from the horizontal. Calculate the distance AC. Give your answer correct to 3 significant figures.

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Question 9
Categorisation: Determine an angle in a 3D diagram.
[Edexcel GCSE(9-1) Mock Set 1 Autumn 2016 3H Q19]
The diagram shows a pyramid with base 𝐴𝐵𝐶 . 𝐶𝐷 is perpendicular to both 𝐶𝐴 and 𝐶𝐵 .
Angle 𝐶𝐵𝐷 = 34° Angle 𝐴𝐷𝐵 = 45° Angle 𝐷𝐵𝐴 = 60° 𝐵𝐶 = 20 cm.

Calculate the size of the angle between the line 𝐴𝐷 and the plane 𝐴𝐵𝐶 .

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Question 10
Categorisation: Using trigonometry twice, both to find a side and an angle.
[Edexcel GCSE Nov2016-2H Q15] AB = 15 m       BC = 24 m        Angle BAD = 62°
Work out the size of angle BCD. Give your answer correct to 1 decimal place.

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Question 11
Categorisation: Use trigonometry in the context of circle theorems.
[Edexcel GCSE Nov2015-2H Q15b]
𝐵 , 𝐶 and 𝐷 are points on the circumference of a circle, centre 𝑂. 𝐵𝑂𝐷 is a diameter of the circle. Calculate the length of 𝐵𝐶 .

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Question 12
Categorisation: Know exact values for 𝒔𝒊𝒏, 𝒄𝒐𝒔, 𝒕𝒂𝒏 of 𝟑𝟎°, 𝟒𝟓° and 𝟔𝟎°.
[Edexcel Specimen Papers Set 1, Paper 1F Q27a, Paper 1H Q7a]
Write down the exact value of 𝑐𝑜𝑠 30°

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Question 13
Categorisation: Use exact trigonometry values to find an unknown side.

Work out the length of 𝐴𝐶 .
Do not use a calculator for this question. 14 / 25

Question 14
Categorisation: Use exact trig values in harder multi-step problems.

[Edexcel GCSE(9-1) Mock Set 3 Autumn 2017 1H Q20 Edited] The diagram shows three right-angled triangles.
Given that 𝑦 = 𝑘𝑛 , find the value of 𝑘 .

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Question 15
Categorisation: Manipulate surds in the context of trigonometry.

[AQA IGCSE FM Jan2013-P1 Q15 Edited] Find the value of 𝑥 .

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Question 16
Categorisation: Determine an unknown angle using trigonometry.

[Edexcel GCSE Nov-2006-4I Q21, Nov2006-6H Q10] Work out the value of 𝑥 .

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Question 17
Categorisation: As above, but where the angle is described rather than necessarily
indicated on the diagram, e.g. “angle 𝑨𝑩𝑪”.

[Edexcel IGCSE Jan2012-3H Q9a] Triangle PQR has a right angle at Q. PQ = 3.4 cm and PR = 5.8 cm.
Work out the size of angle QRP. Give your answer correct to 1 decimal place.

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Question 18
Categorisation: Use trigonometry in the context of bounds.

[Edexcel IGCSE June2010-3H Q14c] Triangle ABC is right-angled at B. AB = 20 cm, correct to 1 significant figure.
BC = 8.3 cm, correct to 2 significant figures.
Calculate the lower bound for the value of 𝑡𝑎𝑛 𝑥°.

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Question 19
Categorisation: Use a combination of Pythagoras theorem and trigonometry to find an unknown angle.

[Edexcel IGCSE Jan2014(R)-3H Q17] The diagram shows triangle ABC.
D is the point on AB, such that CD is perpendicular to AB.
AC = 8.3 cm. AD = 4.7 cm. BD = 7.5 cm.
Calculate the size of angle ABC. Give your answer correct to 1 decimal place.

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Question 20
Categorisation: Determine an angle of elevation.

[Edexcel IGCSE May2015(R)-3H Q23] The height of the flagpole, TX, is 10 m.

Calculate the size of the angle of elevation of T from A.

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Question 21
Categorisation: Determine an angle in a 3D diagram.

[Edexcel IGCSE Jan2017-4H Q21b]
The diagram shows a cuboid ABCDEFGH. AB = 21 cm and CH = 9 cm.
K is the point on EH such that angle AKB = 68° and BK = 16.5 cm.

Calculate the size of the angle between the line BK and the plane ABCD.

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Question 22
Categorisation: As above.

[Edexcel IGCSE Jan2013-3H Q21]
The diagram shows a pyramid with a horizontal rectangular base PQRS.
PQ = 16 cm. QR = 10 cm. M is the midpoint of the line PR.
The vertex, T, is vertically above M. MT = 15 cm. Calculate the size of the angle between TP and the base PQRS.

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Question 23
Categorisation: Use trigonometry in the context of volumes of solids.

[Edexcel GCSE(9-1) Mock Set 3 Autumn 2017 3H Q12]

The diagram shows a metal rod, AB, resting inside a cylindrical tin. The tin is on a horizontal table.
AC is a diameter of the base of the tin.
B is on the top edge of the tin.
BC is vertical.
The radius of the base of the tin is 5 cm.
The volume of the tin is 1178 cm3
.
Find the angle between the rod and the base of the tin.

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Question 24
Categorisation: As above.

[Edexcel IGCSE Jan2014(R)-4H Q21] 25 / 25

Question 25
Categorisation: Use trigonometry in the context of bearings.

[Edexcel IGCSE Jan2015(R)-3H Q11] Town B is 35 km east and 80 km north of town A.

Work out the bearing of town A from town B.