Law of Sines and Law of Cosines Practice

Front

What is the Law of Sines?

Back

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. 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

How do you use the Law of Sines to find an unknown angle?

Back

To find an unknown angle using the Law of Sines, rearrange the formula: sin(A)/a = sin(B)/b. Solve for sin(A) and then use the inverse sine function.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

How do you use the Law of Cosines to find an unknown side?

Back

To find an unknown side using the Law of Cosines, use the formula: c² = a² + b² - 2ab*cos(C). Rearrange to solve for c.

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. Conversely, the smaller the angle, the shorter the opposite side.

Tags

CCSS.HSG.CO.C.10

Front

When is it appropriate to use the Law of Sines?

Back

The Law of Sines is appropriate 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 is it appropriate to use the Law of Cosines?

Back

The Law of Cosines is appropriate 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 formula for finding the area of a triangle using the Law of Sines?

Back

The area (A) of a triangle can be found using the formula: A = (1/2)ab*sin(C), where a and b are two sides and C is the included angle.

Tags

CCSS.HSG.SRT.D.9

Front

How do you round numbers in mathematical problems?

Back

To round a number, look at the digit to the right of the place value you are rounding to. If it is 5 or greater, round up; if it is less than 5, round down.

Tags

CCSS.3.NBT.A.1

CCSS.4.NBT.A.3

Front

What is the significance of rounding in real-world applications?

Back

Rounding is significant in real-world applications to simplify numbers for easier interpretation and communication, especially in measurements and financial calculations.