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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