Sine and Cosine Rule

Front

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).

Front

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).

Front

What does SSS stand for in triangle problems?

Back

SSS stands for 'Side-Side-Side', which means all three sides of a triangle are known.

Front

What does SAS stand for in triangle problems?

Back

SAS stands for 'Side-Angle-Side', which means two sides and the included angle of a triangle are known.

Front

What does AAS stand for in triangle problems?

Back

AAS stands for 'Angle-Angle-Side', which means two angles and one side of a triangle are known.

Front

What does SSA stand for in triangle problems?

Back

SSA stands for 'Side-Side-Angle', which means two sides and a non-included angle of a triangle are known.

Front

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 three sides (SSS) or two sides and the included angle (SAS).

Front

If a = 13.35, b = 12.91, and angle C = 60°, what is the length of side c using the Cosine Rule?

Back

c = √(a² + b² - 2ab*cos(C)) = √(13.35² + 12.91² - 2*13.35*12.91*cos(60°)) = 19.43.

Front

If angle A = 30° and angle B = 45°, what is angle C in a triangle?

Back

Angle C = 180° - (Angle A + Angle B) = 180° - (30° + 45°) = 105°.