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

B: cos

Question 2

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

B: a2 - x2

Question 3

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

Revolt · Accepted Answer

A: Pythagorean theorem

Question 4

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

Revolt · Accepted Answer

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

Question 5

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

Revolt · Accepted Answer

B: ; D:

Question 6

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

Revolt · Accepted Answer

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

Question 7

An observer measures the angle from the ground to the top of a building from two different locations. The measurements are shown on the diagram.What is angle A? degrees

Revolt · Accepted Answer

138

Question 8

A surveyor measures the distance to the two landmarks, as shown in the diagram. What is the distance, d, between the landmarks?

Revolt · Accepted Answer

A: 123 m

Question 9

✔ b2 - 2bx + x2b2 + x2

Revolt · Accepted Answer

A: b2 - 2bx + x2

Question 10

2) h2 = a2 - x2

Revolt · Accepted Answer

B: Rearrange the previous statement

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

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