CK-12-Pre-Calculus Concepts

4.5. Law of Cosines http://www.ck12.org

c^2 =a^2 +b^2 − 2 ab·cosC

2302 = 1202 + 1502 − 2 · 120 · 150 ·cosD

2302 − 1202 − 1502 =− 2 · 120 · 150 ·cosD

2302 − 1202 − 1502

− 2 · 120 · 150 =cosD

D=cos−^1

( 2302 − 1202 − 1502

− 2 · 120 · 150

)

≈ 116. 4 ◦≈ 2. 03 radians

Example B
Determine the length of sidep.

Solution:

c^2 =a^2 +b^2 − 2 ab·cosC

p^2 = 2122 + 3882 − 2 · 212 · 388 ·cos 82◦

p^2 ≈ 194192. 02 ...

p≈ 440. 7

Example C
Determine the degree measure of angleN.