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

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

✔ b2 - 2bx + x2b2 + x2

+2bx✔ -2bx

4) c2 = h2 + 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

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

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

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

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

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

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

2) h2 = a2 - x2

What is angle B? degrees

3) c2 = h2 + (b-x)2

What is the length of side x? 25 m31 m44 m✔ 47 m

How tall is the building? 25 m✔ 31 m44 m47 m