The Cosine Rule worksheet
7 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.
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4 marks
In triangle \(ABC\), \(AB = 9\) cm, \(BC = 16\) cm and angle \(ABC = 127^\circ\).
(a)Write down which of the sine rule and the cosine rule you would use to work out the length of \(AC\).
(b)Work out the length of \(AC\).
Give your answer to 1 decimal place.
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3 marks
\(ABC\) is a triangle.
Find the size of the angle marked \(x\).
Give your answer to 1 decimal place.
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4 marks
Two straight paths leave a youth hostel. The angle between them is \(101^\circ\).
Zainab walks \(11\) km along one path. Oscar walks \(13\) km along the other.
Work out the distance between Zainab and Oscar.
Give your answer to 1 decimal place.
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4 marks
A triangular car park at a garden centre has sides
\(AB = 30\) m, \(BC = 55\) m and \(AC = 45\) m.
Work out the size of the largest angle of the car park.
Give your answer correct to 1 decimal place.
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4 marks
In triangle \(ABC\), \(AB = 12\) cm, \(BC = 13\) cm and angle \(ABC = 119^\circ\).
(a)Write down which of the sine rule and the cosine rule you would use to work out the length of \(AC\).
(b)Work out the length of \(AC\).
Give your answer correct to 1 decimal place.
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3 marks
\(ABC\) is a triangle.
Calculate the size of the angle marked \(x\).
Give your answer correct to 1 decimal place.
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4 marks
Two straight paths leave a campsite. The angle between them is \(60^\circ\).
Amara walks \(12\) km along one path. Ben walks \(9\) km along the other.
Calculate the distance between Amara and Ben.
Give your answer correct to 1 decimal place.
Answers
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(a) the cosine rule
(b) \(22.6\ \text{cm}\) - \(41.8^\circ\)
- \(18.6\ \text{km}\)
- \(92.1^\circ\)
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(a) the cosine rule
(b) \(21.5\ \text{cm}\) - \(91.0^\circ\)
- \(10.8\ \text{km}\)