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.
Topics covered:
Worksheet Preview
Full preview • 11 questions
Mastering Sine & Cosine Rules
Subject: MathematicsGrade: GCSE Higher
Name:
Date:
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]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Related Worksheets
Details
- Created
- 12/30/2025
- Updated
- 12/30/2025
- Type
- worksheet