Geometry 8.5 Law of Sines 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. It is expressed as: 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 or angle in a triangle when the Law of Sines cannot be applied. It is expressed as: c² = a² + b² - 2ab*cos(C).

Front

When would you use the Law of Sines?

Back

You would 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 would you use the Law of Cosines?

Back

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

Front

How do you find the length of a side using the Law of Sines?

Back

To find the length of a side using the Law of Sines, rearrange the formula a/sin(A) = b/sin(B) = c/sin(C) to solve for the desired side length.

Front

How do you find an angle using the Law of Sines?

Back

To find an angle using the Law of Sines, rearrange the formula to isolate the sine of the angle, then use the inverse sine function (sin⁻¹) to find the angle.

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

How do you find the length of a side using the Law of Cosines?

Back

To find the length of a side using the Law of Cosines, rearrange the formula c² = a² + b² - 2ab*cos(C) to solve for the desired side length.

Front

How do you find an angle using the Law of Cosines?

Back

To find an angle using the Law of Cosines, rearrange the formula to isolate the cosine of the angle, then use the inverse cosine function (cos⁻¹) to find the angle.

Front

What is the relationship between the sides and angles in a triangle?

Back

In a triangle, the larger the angle, the longer the opposite side. Conversely, the smaller the angle, the shorter the opposite side.