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 of the triangle. It can be expressed as: a/sin(A) = b/sin(B) = c/sin(C).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

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 expressed as: c² = a² + b² - 2ab*cos(C).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

When do you use the Law of Sines?

Back

The Law of Sines is used when you have either two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

When do you use the Law of Cosines?

Back

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

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

What is the formula for the Law of Cosines?

Back

c² = a² + b² - 2ab*cos(C).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

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 = b*sin(A)/sin(B).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

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

Back

In a triangle, the larger the angle, the longer the opposite side. This relationship is fundamental in both the Law of Sines and the Law of Cosines.

Tags

CCSS.HSG.CO.C.10

Front

What is the sine of an angle in a right triangle?

Back

In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

Tags

CCSS.HSG.SRT.C.6

Front

What is the cosine of an angle in a right triangle?

Back

In a right triangle, the cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Tags

CCSS.HSG.SRT.C.6

Front

How can you determine if a triangle is valid with given sides?

Back

A triangle is valid if the sum of the lengths of any two sides is greater than the length of the third side (Triangle Inequality Theorem).