Law of Sines and Law of Cosines — a Deeper Look

Question 1

Use the diagram to derive the law of cosines.Which of the following statements is true?

Revolt · Accepted Answer

cos

Question 2

✔ b2 - 2bx + x2b2 + x2

Revolt · Accepted Answer

b2 - 2bx + x2

Question 3

+2bx✔ -2bx

Revolt · Accepted Answer

-2bx

Question 4

4) c2 = h2 + b2 -2bx + x2

Revolt · Accepted Answer

Expand (b – x)2

Question 5

Question 5

Revolt · Accepted Answer

1) a2 = h2 + x2 2) h2 = 3) c2 = h2 + (b − x)2 4) c2 = h2 + 5) c2 = a2 − x2 + b2 − 2bx + x2 6) c2 = a2 + b2 7) x = acosC 8) c2 = a2 + b22abcosC: a2 - x2; 1) a2 = h2 + x2 2) h2 = 3) c2 = h2 + (b − x)2 4) c2 = h2 + 5) c2 = a2 − x2 + b2 − 2bx + x2 6) c2 = a2 + b2 7) x = acosC 8) c2 = a2 + b22abcosC: b2 - 2bx + x2; 1) a2 = h2 + x2 2) h2 = 3) c2 = h2 + (b − x)2 4) c2 = h2 + 5) c2 = a2 − x2 + b2 − 2bx + x2 6) c2 = a2 + b2 7) x = acosC 8) c2 = a2 + b22abcosC: -2bx

Question 6

1) a2 = h2 + x2 2) h2 = 3) c2 = h2 + (b − x)2 4) c2 = h2 + 5) c2 = a2 − x2 + b2 − 2bx + x2 6) c2 = a2 + b2 7) x = acosC 8) c2 = a2 + b22abcosC

Revolt · Accepted Answer

a2 - x2; Selection 1: a2 - x2; Selection 2: b2 - 2bx + x2; Selection 3: -2bx

Question 7

Choose the correct reason to justify each of the first four statements in the derivation.1) a2 = h2 + x2

Revolt · Accepted Answer

Pythagorean theorem

Question 8

Which of the following statements are true? Check all of the boxes that apply.

Revolt · Accepted Answer

Segment h divides triangle ABC into two right triangles.; c2 = h2 + b2 - 2bx + x2; If you know sides a, b, and c, you can find all the angles of triangle ABC.

Question 9

Which of the following statements are useful in deriving the law of sines? Check all of the boxes that apply.

Revolt · Accepted Answer

Answer image: https://r07.core.learn.edgenuity.com//media.edgenuity.com/EVresources/6129-01-12-20-05-task/mr001-1.jpg; Answer image: https://r07.core.learn.edgenuity.com//media.edgenuity.com/EVresources/6129-01-12-20-05-task/mr001-3.jpg

Question 10

Which of the following statements are true? Check all of the boxes that apply.

Revolt · Accepted Answer

Sine A = StartFraction h over c EndFraction; b sinA = a sinB; StartFraction a over sine A EndFraction = StartFraction b over sine B EndFraction; StartFraction b over sine B EndFraction = StartFraction c over sine C EndFraction

Law of Sines and Law of Cosines — a Deeper Look Answers

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