Mastering Sine & Cosine Rules

Mathematics
Year 9
12 questions
~24 mins
0 views0 downloads

About This Worksheet

A worksheet covering Sine & Cosine Rules for Year 9 students.

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Mastering Sine & Cosine Rules

Subject: MathematicsGrade: Year 9
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Untitled Worksheet

Grade Year 9
A

Practice Questions

Answer all questions. Show your working in the grid spaces provided.
1.
In triangle ABC, side AB = 7 cm, side AC = 10 cm, and angle A = 60°. Use the Cosine Rule to find the length of side BC.
[3 marks]
2.
Calculate the length of side AC in triangle PQR if PQ = 8 cm, PR = 6 cm, and the included angle P = 45°. Use the Cosine Rule.
[3 marks]
3.
In triangle XYZ, side XY = 5 cm, side XZ = 9 cm, and angle X = 40°. Find the length of side YZ using the Cosine Rule.
[3 marks]
4.
In triangle DEF, side DE = 12 cm, side DF = 15 cm, and angle D = 75°. Find side EF using the Cosine Rule.
[3 marks]
5.
Calculate the height of a triangle with sides 8 cm and 10 cm, and included angle 60°, using the Sine Rule to find the height.
[3 marks]
6.
In triangle GHI, sides GI = 9 cm, GH = 7 cm, and angle G = 50°. Use the Sine Rule to find the length of side HI.
[3 marks]
7.
A triangle has sides of 6 cm, 8 cm, and 10 cm. Determine whether the triangle is acute, right-angled, or obtuse.
[2 marks]
8.
In triangle JKL, sides JL = 9 cm, KL = 12 cm, and angle J = 60°. Use the Cosine Rule to find side JK.
[3 marks]
9.
A surveyor measures a triangle with sides 50 m, 60 m, and 70 m. Determine if the triangle is acute, right-angled, or obtuse.
[2 marks]
10.
A boat is sailing from point A to point B, 100 km apart. The bearing is 045°, and the boat is sailing at an angle where the Sine Rule can be used to find the distance to a point C located inland. If the angle at A is 30°, find the distance AC.
[4 marks]
11.
A ladder leans against a wall, forming a 75° angle with the ground. The foot of the ladder is 4 meters from the wall. Use the Sine Rule to find the length of the ladder.
[3 marks]
12.
A triangular plot of land has sides of 30 m, 40 m, and 50 m. Calculate the area of the land using Heron's formula as an application of the Cosine Rule and Sine Rule.
[4 marks]

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Details

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