Mastering Sine & Cosine Rules

Mathematics
Grade 6
1 questions
~2 mins
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About This Worksheet

A worksheet covering Sine & Cosine Rules for Grade 6 students.

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Mastering Sine & Cosine Rules

Subject: MathematicsGrade: Grade 6
Name:
Date:

Untitled Worksheet

Grade Grade 6
A

Introduction

Read the brief explanation below.
1.
The Sine Rule states that in any triangle, the ratio of a side length to the sine of its opposite angle is constant: asinA=bsinB=csinC \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} . The Cosine Rule relates the sides and an included angle: c2=a2+b22abcosC c^2 = a^2 + b^2 - 2ab \cos C .
[4 marks]
B

Procedural / Fluency Questions

Answer the following to practice basic understanding.
1.
In triangle ABC, side a = 10 cm, and angle A = 30°. Use the Sine Rule to find side b if angle B is 45°.
[3 marks]
2.
Given triangle XYZ with sides x=8 cm, y=6 cm, and angle X=60°, find angle Y using the Cosine Rule.
[3 marks]
3.
In triangle PQR, side p = 7 cm, side q = 9 cm, and included angle PQR = 120°. Find side r using the Cosine Rule.
[3 marks]
4.
If in triangle DEF, side d = 12 cm, side e = 15 cm, and angle D = 45°, find the third side f using the Cosine Rule.
[3 marks]
5.
Using the Sine Rule, find angle C in a triangle where sides a=9 cm, b=12 cm, and angle A=40°.
[3 marks]
C

Reasoning / Problem-Solving Questions

Apply the concepts to solve these questions.
1.
In triangle GHI, side g=7 cm, side h=10 cm, and angle G=50°. Use the Cosine Rule to find the third side i.
[4 marks]
2.
A surveyor measures two sides of a triangular plot: 20 m and 25 m, with the included angle 60°. Find the third side using the Cosine Rule.
[4 marks]
3.
In triangle JKL, side j=8 cm, side k=15 cm, and angle J=70°. Find angle K using the Sine Rule.
[4 marks]
4.
A kite has diagonals of lengths 10 m and 24 m, intersecting at right angles. Using the Sine & Cosine Rules, estimate the lengths of its sides.
[5 marks]
5.
A tower leans such that the angle of elevation to the top from a point 30 meters away is 45°. Using the Sine or Cosine Rule, estimate the height of the tower.
[5 marks]

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Details

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