Please help with trig

Question

Emy is trying to build a fence around her triangular garden. She only has one side left to build. The

other two sides are 38 feet and 19 feet long and the shared angle is 130 deg. What is the length of the

last side of the garden?

Answer 1

use the Law of Cosines to find the side opposite the given angle

c=a^2 + b^2 -2abCosC

c^2=38^2 + 19^2 -2(38)(19)Cos130

= 1444 +361 -1444(-.643)

=1805 + 928.2 =2733.2

c = sqr2733.2 = about 52.3 feet =the 3rd side length

or another method, or check the answer

construct a right trianlge with height 29.11

38sin130= 29.2

base =43.3

c^2 = sum of squares

c = sqruare root of sum of squares = about 52.3