Mastering Sine & Cosine Rules

Mathematics
GCSE Higher
11 questions
~22 mins
0 views0 downloads

About This Worksheet

A worksheet covering Sine & Cosine Rules for GCSE Higher students. It includes basic questions to test understanding and advanced problems to develop reasoning skills.

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Mastering Sine & Cosine Rules

Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet

Grade GCSE Higher
A

Practice Questions

Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the length of side AB in triangle ABC, where angle C is 40°, side AC is 10 cm, and side BC is 12 cm. Use the Law of Cosines.
[3 marks]
2.
In triangle PQR, angle P is 60°, side PQ is 8 cm, and side PR is 10 cm. Find the length of QR using the Law of Cosines.
[3 marks]
3.
In triangle XYZ, side XY = 7 cm, side XZ = 9 cm, and angle X = 50°. Calculate the length of side YZ.
[3 marks]
4.
Calculate the measure of angle A in triangle DEF, where sides DE = 13 cm, DF = 15 cm, and side EF = 20 cm. Use the Law of Cosines.
[3 marks]
5.
Given a triangle with sides 8 cm, 15 cm, and 17 cm, determine whether the triangle is right-angled.
[2 marks]
6.
In triangle GHI, angle G is 70°, side GH is 9 cm, and side GI is 11 cm. Find the measure of angle H using the Law of Cosines.
[3 marks]
7.
Using the Law of Sines, find angle J in triangle JKL if side JL = 10 cm, side JK = 15 cm, and angle K is 45°.
[3 marks]
8.
A ladder leans against a wall, forming a 75° angle with the ground. If the ladder is 6 meters long, how high does it reach on the wall? Use sine rule where appropriate.
[3 marks]
9.
In a triangle with sides 9, 12, and 15, find the largest angle using the Law of Cosines.
[3 marks]
10.
A surveyor measures a triangle where two sides are 50 m and 80 m, with an included angle of 60°. Calculate the third side using the Law of Cosines.
[3 marks]
11.
A boat is sailing from point A to point B 30 km apart. The bearing from A to B is 045°, and the boat heads directly towards a lighthouse 20 km east of point A. Use the Law of Sines to find the distance from the boat’s current position to the lighthouse.
[4 marks]

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Details

Created
12/30/2025
Updated
12/30/2025
Type
worksheet