Sine and Cosine Rule

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What is the Sine Rule?

Back

The Sine Rule states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. It is expressed as: a/sin(A) = b/sin(B) = c/sin(C).

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What is the Cosine Rule?

Back

The Cosine Rule relates the lengths of the sides of a triangle to the cosine of one of its angles. It is expressed as: c² = a² + b² - 2ab*cos(C).

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When should you use the Sine Rule?

Back

Use the Sine Rule when you have either two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA).

Front

When should you use the Cosine Rule?

Back

Use the Cosine Rule when you have either two sides and the included angle (SAS) or all three sides (SSS) of a triangle.

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What is the formula for the Sine Rule?

Back

The formula for the Sine Rule is: a/sin(A) = b/sin(B) = c/sin(C).

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What is the formula for the Cosine Rule?

Back

The formula for the Cosine Rule is: c² = a² + b² - 2ab*cos(C).

Front

Find the value of c if a = 10, b = 15, and angle C = 60° using the Cosine Rule.

Back

c = √(10² + 15² - 2*10*15*cos(60°)) = 24.7.

Front

Find the missing side x if a = 5, b = 7, and angle C = 45° using the Sine Rule.

Back

x = (b * sin(A)) / sin(B) where A and B can be calculated using the Sine Rule.

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What does 'SSA' stand for in triangle problems?

Back

'SSA' stands for Side-Side-Angle, a condition where two sides and a non-included angle are known.

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What does 'SAS' stand for in triangle problems?

Back

'SAS' stands for Side-Angle-Side, a condition where two sides and the included angle are known.