Exploring the Law of Sines and Law of Cosines

What is required to extend the use of sine and cosine to non-right triangles?

• Right triangle properties

• Pythagorean theorem

• Algebraic equations

• Law of Sines and Law of Cosines

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

In triangle ABC, if angle A is 48 degrees and side a is unknown, which law would you use to find side a?

• Pythagorean theorem

• Law of Cosines

• Law of Sines

• None of the above

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is the correct approach to solve for side lengths using the Law of Sines?

• Using Pythagorean theorem

• Using algebraic simplification only

• Using all three angle-side ratios

• Using only the known angle-side ratios

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Which formula represents the Law of Cosines?

• a/b = sin(A)/sin(B)

• sin(A)/a = sin(B)/b = sin(C)/c

• a^2 = b^2 + c^2

• a^2 = b^2 + c^2 - 2bc * cos(A)

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

How do you solve for side b using the Law of Cosines when you know sides a, c, and angle B?

• None of the above

• b = sqrt(a^2 + c^2 - 2ac * cos(B))

• b^2 = a^2 + c^2 - 2ac * cos(B)

• b = a^2 + c^2 - 2ac * cos(B)

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What does the Law of Cosines reduce to when the angle is a right angle?

• Pythagorean theorem

• Law of Sines

• It does not reduce

• Algebraic identity

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

When solving for a side using the Law of Cosines, what is crucial to ensure correct results?

• None of the above

• Adding the sides first

• Multiplying the sides first

• Using the correct angle for the formula

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Which scenario requires the use of the Law of Cosines?

• When two angles and one side are known

• When all sides and no angles are known

• When two sides and the included angle are known

• When all angles and no sides are known

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is the first step in using the Law of Cosines to solve for a side?

• Divide the known sides by the cosine of the known angle

• Square the known sides

• Multiply the known sides by the cosine of the known angle

• Identify the known angle opposite the side to solve

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

How do you verify the correctness of your solution in trigonometry problems?

• Check if the sides satisfy the triangle inequality

• Re-calculate using a different method

• Consult the textbook solutions

• All of the above