Deriving the Law of Cosines

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Follow these steps to derive the law of cosines.

✓ 1. The relationship between the side lengths in AABD is

C2 = x2 +hby the Pythagorean theorem M

✓ 2. The relationship between the side lengths in ACBD is

Q2 = (b – x)2 +hby the Pythagorean theorem

V 3. The equation e? = (6 – x)2 + h? is expanded y to become

22 = 62 – 2x + x2 +h?

a

h

✓ 4. Using the equation from step 1, the equation

22 = 62 – 2bx +32+ hbecomes a = 62 – 2bx + 2

by substitution

A

х

D

b-x

С

Correct! You have completed this exercise.

b

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Answer:

1 – pythagorean theorem

2- pythagorean theorem

3- expanded

4- substitution

5- cos (A)

6- c

7-c cos(A)

8- rearranging

Step-by-step explanation:

edg 2020