Chapter 7 - Applications of Trigonometry and Vectors - Section 7.3 The Law of Cosines - 7.3 Exercises - Page 325: 77

$a = \sqrt{34}$ $b = \sqrt{29}$ $c = \sqrt{13}$

$A = (2,5)$ $B = (-1,3)$ $C = (4,0)$ We can find the length of side $a$: $a = \sqrt{(4-(-1))^2+(0-3)^2}$ $a = \sqrt{34}$ We can find the length of side $b$: $b = \sqrt{(4-2)^2+(0-5)^2}$ $b = \sqrt{29}$ We can find the length of side $c$: $c = \sqrt{(2-(-1))^2+(5-3)^2}$ $c = \sqrt{13}$