Sine and Cosine Rules

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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 can be expressed as: a/sin(A) = b/sin(B) = c/sin(C).

Front

When should you use the Sine Rule?

Back

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

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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 can be expressed as: c² = a² + b² - 2ab cos(C).

Front

When should you use the Cosine Rule?

Back

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

Front

How many parts do you need to equate when using the Sine Rule?

Back

You need to equate 2 parts.

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What is the formula for the Sine Rule?

Back

The Sine Rule can be expressed as: a/sin(A) = b/sin(B) = c/sin(C).

Front

What does 'a' represent in the Sine Rule?

Back

'a' represents the length of one side of the triangle.

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What does 'A' represent in the Sine Rule?

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'A' represents the angle opposite to side 'a'.

Front

What is the relationship between the sides and angles in a triangle according to the Sine Rule?

Back

The ratio of the length of a side to the sine of its opposite angle is constant for all three sides and angles.

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What is the significance of the Cosine Rule in triangle calculations?

Back

The Cosine Rule allows you to find a side length or an angle when you have sufficient information about the other sides and angles.