Law of Sines & Cosines

Front

What is the Law of Sines?

Back

The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides and angles in the triangle.

Front

What is the Law of Cosines?

Back

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It is used to find a side when two sides and the included angle are known.

Front

What are the trigonometric ratios?

Back

The trigonometric ratios are relationships between the angles and sides of a right triangle: Sine (sin), Cosine (cos), and Tangent (tan). They can be remembered using 'Soh Cah Toa'.

Front

How do you remember the trigonometric ratios?

Back

You can remember the trigonometric ratios using the mnemonic 'Soh Cah Toa': Soh = Sin = Opposite/Hypotenuse, Cah = Cos = Adjacent/Hypotenuse, Toa = Tan = Opposite/Adjacent.

Front

What is the formula for the Law of Sines?

Back

The formula for the Law of Sines is: (a/sin(A)) = (b/sin(B)) = (c/sin(C)), where a, b, and c are the sides of the triangle and A, B, and C are the angles opposite those sides.

Front

What is the formula for the Law of Cosines?

Back

The formula for the Law of Cosines is: c² = a² + b² - 2ab*cos(C), where c is the side opposite angle C, and a and b are the other two sides.

Front

When do you use the Law of Sines?

Back

You use the Law of Sines when you have either two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA) in a triangle.

Front

When do you use the Law of Cosines?

Back

You use the Law of Cosines when you have two sides and the included angle (SAS) or all three sides (SSS) of a triangle.

Front

What is the sine of 30 degrees?

Back

The sine of 30 degrees is 0.5.

Front

What is the cosine of 60 degrees?

Back

The cosine of 60 degrees is 0.5.