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 + x2Pythagorean theoremRearrange the previous statementAssumption✔ Expand (b – x)2

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

x2 - a2✔ a2 - x2

Revolt · Accepted Answer

✔ 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: 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 7

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

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

Answer image: //media.edgenuity.com/EVresources/6129-01-12-20-06-task/mr001-1.jpg; b sinA = a sinB; Answer image: //media.edgenuity.com/EVresources/6129-01-12-20-06-task/mr001-2.jpg; Answer image: //media.edgenuity.com/EVresources/6129-01-12-20-06-task/mr001-3.jpg

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

More from this Course

TRY EDGENUITY HACKS