"Full Coverage": Trigonometry of Right-Angled Triangles

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1 "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 /homework, logging on, Practise Past Papers/Worksheets (or Library Past/Past Papers for teachers), and using the Revision tab. 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. Give your answer correct to 3 significant figures.... cm 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.... cm

2 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. Give your answer correct to 3 significant figures.... cm 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. y =... km

3 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.... m 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. QR =... cm

4 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.... cm 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. [Edexcel IGCSE June2010-3H Q20] A, B and C are points on horizontal ground. C is due West of B. A is due South of B and AB = 40 m. There is a vertical flagpole at B. From A, the angle of elevation of the top of the flagpole is 13 From C, the angle of elevation of the top of the flagpole is 19 Calculate the distance AC. Give your answer correct to 3 significant figures.... m

5 Question 9 Categorisation: Determine an angle in a 3D diagram. [Edexcel GCSE(9-1) Mock Set 1 Autumn H 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. Give your answer correct to 1 decimal place.

6 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. 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. Give your answer correct to 3 significant figures.... cm

7 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 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. AC =... cm

8 Question 14 Categorisation: Use exact trig values in harder multi-step problems. [Edexcel GCSE(9-1) Mock Set 3 Autumn H Q20 Edited] The diagram shows three right-angled triangles. Given that y = kn, find the value of k....

9 Question 15 Categorisation: Manipulate surds in the context of trigonometry. [AQA IGCSE FM Jan2013-P1 Q15 Edited] Find the value of x. x = Question 16 Categorisation: Determine an unknown angle using trigonometry. [Edexcel GCSE Nov I Q21, Nov2006-6H Q10] Work out the value of x. Give your answer correct to 1 decimal place.

10 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. 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....

11 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.

12 Question 20 Categorisation: Determine an angle of elevation. [Edexcel IGCSE May2015(R)-3H Q23] The height of the flagpole, TX, is 10 m. A, B and C are points on horizontal ground. B is due North of A and AB is 14 m. C is due East of A and AC is 25 m. A vertical flagpole, TX, has its base at the point X on BC such that the angle AXC is a right angle. Calculate the size of the angle of elevation of T from A. Give your answer correct to 1 decimal place. Question 21 Categorisation: Determine an angle in a 3D diagram. [Edexcel IGCSE Jan2017-4H Q21b] The diagram shows a cuboid ABCDEFGH.

13 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. Give your answer correct to 1 decimal place. 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. Give your answer correct to 1 decimal place.

14 Question 23 Categorisation: Use trigonometry in the context of volumes of solids. [Edexcel GCSE(9-1) Mock Set 3 Autumn H 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 cm 3. Find the angle between the rod and the base of the tin. Give your answer correct to the nearest degree.

15 Question 24 Categorisation: As above. [Edexcel IGCSE Jan2014(R)-4H Q21] The diagram shows a solid cone. The base of the cone is a horizontal circle, centre O, with radius 4.5 cm. AB is a diameter of the base and OV is the vertical height of the cone. The curved surface area of the cone is 130 cm 2. Calculate the size of the angle AVB. Give your answer correct to 1 decimal place. 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. Give your answer correct to the nearest degree.

16 Answers Question cm Question cm Question cm Question 4 y = 14.9 km Question m Question 6 QR = 9.12 cm Question 7 any value in the range 16.4 cm to 16.5 cm Question m Question 9 any value in the range 38.5 to 38.6 Question Question 11 any value in the range 2.74 cm to 2.75 cm Question Question 13 AC = 3 cm Question 14 k = 3 4 Question 15 x = 60 Question Question Question Question Question Question Question Question Question Question