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.

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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.
Given a triangle with sides a = 7 cm, b = 10 cm, and included angle C = 60°, use the Cosine Rule to find side c.
[3 marks]
2.
In triangle ABC, angle A = 45°, side a = 8 cm, and side b = 10 cm. Use the Sine Rule to find side c.
[3 marks]
3.
Calculate the size of angle B in a triangle where sides a = 9 cm, b = 12 cm, and side c = 15 cm, using the Cosine Rule.
[3 marks]
4.
In triangle PQR, side PQ = 11 cm, side PR = 13 cm, and angle Q = 70°. Use the Cosine Rule to find side QR.
[3 marks]
5.
A triangle has sides of 5 cm and 8 cm with an included angle of 120°. Calculate the third side using the Cosine Rule.
[3 marks]
6.
In triangle XYZ, side x = 6 cm, side y = 9 cm, and angle Z = 50°. Use the Sine Rule to find angle Y.
[3 marks]
7.
A triangle has sides 7 cm, 24 cm, and 25 cm. Use the Cosine Rule to determine if it is a right-angled triangle.
[2 marks]
8.
In triangle DEF, sides d = 10 cm, e = 15 cm, and angle D = 60°. Find the length of side f using the Cosine Rule.
[3 marks]
9.
A boat is anchored at a point where the angles of elevation to two lighthouses are 40° and 60°. The distance between the lighthouses is 100 meters. Use the Sine Rule to estimate the distance from the boat to each lighthouse.
[4 marks]
10.
A satellite is in a triangular orbit with sides of 12 km, 16 km, and 20 km. Use the Cosine Rule to find the measure of the largest angle in the triangle.
[3 marks]
11.
A ladder leans against a wall forming a 75° angle with the ground. The ladder reaches 4 meters high. Calculate the length of the ladder using trigonometry.
[3 marks]

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Details

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