A fence post is 52.0m from where you are standing, in a direction of 37 degree north of east.A second fence post is due south from you.what is the distance of the second post from you if the distance b/w the two post is 80.0m

Answer 1

from where you are standing, the angle between the fence posts is
... 37º + 90º = 127º

use the law of sines to find the angle between you and the 1st post
... measured from the 2nd post

sin(Θ) / 52.0 = sin(127º) / 80.0

the angle (α) between you and the 2nd post, measured from the 1st post is
... α = 180º - 127º - Θ

use the law of sines (again) to find the distance b/w you and the 2nd post

d / sin(α) = 80.0 / sin(127º)

Answer 2

using the law of cosines,
80^2 = x^2 + 52^2 - 104x cos127º
x = 37