College Algebra & Trigonometry, 2018a

488 CHAPTER 11. THE LAW OF SINES THE LAW OF COSINES
(a cos C, a sin C)
B
a
y
c
C
x
D
A
(b, 0)
Using the distance formula, we can say that:
c = √ (a cos C − b) 2 +(a sin C − 0) 2
Squaring both sides:
c 2 =(a cos C − b) 2 +(a sin C − 0) 2
and
c 2 = a 2 cos 2 C − 2ab cos C + b 2 + a 2 sin 2 C
or
c 2 = a 2 sin 2 C + a 2 cos 2 C + b 2 − 2ab cos C