Law of Cosines

Front

What is the Law of Cosines used for?

Back

The Law of Cosines is used to find a side or angle in a triangle when two sides and the included angle are known, or when all three sides are known.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

State the Law of Cosines formula.

Back

The Law of Cosines formula is: c² = a² + b² - 2ab * cos(C), where a and b are the lengths of the sides, C is the included angle, and c is the side opposite angle C.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

When should you use the Law of Cosines instead of the Law of Sines?

Back

Use the Law of Cosines when you have 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 Law of Sines used for?

Back

The Law of Sines is used to find unknown angles or sides in a triangle 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.11

CCSS.HSG.SRT.D.10

Front

State the Law of Sines formula.

Back

The Law of Sines formula is: a/sin(A) = b/sin(B) = c/sin(C), where a, b, and c are the lengths of the sides opposite angles A, B, and C respectively.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

What is the relationship between the angles and sides in a triangle according to the Law of Sines?

Back

The ratio of the length of a side to the sine of its opposite angle is constant for all three sides and angles in a triangle.

Tags

CCSS.HSG.SRT.D.11

CCSS.HSG.SRT.D.10

Front

How do you find the missing side using the Law of Cosines?

Back

To find a missing side using the Law of Cosines, rearrange the formula to solve for the unknown side, substituting the known values for the other sides and the included angle.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

What is the significance of the included angle in the Law of Cosines?

Back

The included angle is the angle between the two known sides, and it is essential for applying the Law of Cosines to find the unknown side.

Tags

CCSS.HSG.SRT.D.11

CCSS.HSG.SRT.D.10

Front

How can you determine if a triangle is obtuse using the Law of Cosines?

Back

If the square of the longest side is greater than the sum of the squares of the other two sides (c² > a² + b²), the triangle is obtuse.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

What is the first step in solving a triangle using the Law of Cosines?

Back

Identify which sides and angles are known and determine if the Law of Cosines is applicable based on the given information.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11