Laws of Sine and Cosine

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. Formula: a/sin(A) = b/sin(B) = c/sin(C).

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. Formula: c² = a² + b² - 2ab*cos(C).

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

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).

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).

Front

If A = 37°, a = 8, b = 14, how many triangles can be formed?

Back

No triangles can be formed.

Front

Given A = 45°, B = 65°, c = 25, find a.

Back

a ≈ 18.8.

Front

What does it mean if the Law of Sines gives no solution?

Back

It means that the given information does not correspond to a valid triangle configuration.

Front

What is an ambiguous case in the Law of Sines?

Back

An ambiguous case occurs when using the Law of Sines with SSA (two sides and a non-included angle), which can result in zero, one, or two possible triangles.