GCSE Grade B Trigonometry Exam Questions
GCSE Grade B Trigonometry Exam Questions
1. In triangle ABC, AB = 5 cm, angle BAD = 49°, DC = 4.5 cm, BD is perpendicular to AC.
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(a) Calculate the length of BD.
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(2)
(b) Calculate the size of the angle ABC.
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(4)
2. A ladder leans against the side of a house.
The ladder is 4.5 m in length.
(a) The ladder makes an angle of 74° with the ground.
How high up the wall will it reach? (marked x in the diagram)
Give your answer to an appropriate degree of accuracy.
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(4)
(b) The same ladder is now placed 0.9 m away from the side of the house.
What angle does the ladder now make with the ground? (marked y in the diagram)
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(3)
3. An aeroplane is flying from Leeds (L) to London Heathrow (H).
It flies 150 miles on a bearing 136º to a point A.
It then turns through 90º and flies the final 80 miles to H.
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(a) (i) Show clearly why the angle marked x is equal to 46º.
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(ii) Give the bearing of H from A.
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(3)
(b) Use Pythagoras’ Theorem to calculate the distance LH.
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(2)
(c) (i) Calculate the size of the angle marked y.
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(ii) Work out the bearing of L from H.
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(4)
4. In the diagram BC is parallel to AE.
Angle ABC = angle ADE = 90°.
AB = 5 cm, BC = 9 cm, DE = 3 cm.
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(a) Use Pythagoras’ theorem to calculate the length of AC.
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(2)
(b) Explain why triangles ABC and EDA are similar.
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(1)
(c) Use this fact to calculate the length of AD.
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(2)
(d) Calculate the angle marked x in the diagram.
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(4)
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