Question 1195043
Two sides of a triangle field measure 325 meters and 278 meters. 
If these sides form an angle of 47°40’, what is the length of the fence that will surround the field?
:
Find the side opposite the angle
Change 47' 40" to 47 + 40/60 = 47.67 degrees

use the law of cosines here: a^2 = b^2 + c^2 - 2bc Cos(A) where,
a = side opposite 47.67 degrees
b = 325 m
c= 278 m
A = 47.67 degrees
:
a^2 = 325^2 + 287^2 - 2(325*287) Cos(27.67)
a^2 = 105625 + 82369 - 186550 * .8856
a^2 = 187994 - 125662.7
a = {{{sqrt(62371.3)}}}
a = 249.7 meters is the 3rd side
then
325 + 287 + 249.7 = 861.7 meters to surround the field