5.3.4 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 its opposite angle 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

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).

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

Solve for 'a' if: A = 70°, b = 10, and c = 4.

Back

a = 9.4

Front

Solve for 'C' if: a = 9.4, b = 10, and c = 4.

Back

C = 23.5°

Front

What happens if the given sides and angles do not form a triangle?

Back

If the given sides and angles do not satisfy the triangle inequality or the conditions of the Law of Sines or Cosines, it results in 'No Triangle (Error)'.

Front

What is the sine of an angle in a triangle?

Back

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

Front

What is the cosine of an angle in a triangle?

Back

The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

If C = 100°, a = 2, and c = 1, what is the result?

Back

No Triangle (Error)