Sine & Cosine Laws

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 or angle in a triangle when the Law of Sines cannot be applied.

Front

When do you use the Law of Sines?

Back

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).

Front

When do you use the Law of Cosines?

Back

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

Front

Find angle A if a = 10, b = 7, and C = 30° using the Law of Sines.

Back

Angle A = 41.7°.

Front

Find side c if a = 5, b = 6, and angle C = 60° using the Law of Cosines.

Back

Side c = 7.2.

Front

What is the formula for the Law of Sines?

Back

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

Front

What is the formula for the Law of Cosines?

Back

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

Front

If angle A = 30° and angle B = 60°, what is angle C?

Back

Angle C = 90° (since the sum of angles in a triangle is 180°).

Front

How do you find the area of a triangle using the Law of Sines?

Back

Area = (1/2) * a * b * sin(C).