Question

The three ropes in the figure are tied to a small, very light ring. Two of these ropes are anchored to walls at right angles with tensions T1 = 20 N and T2 = 60 N. What are the magnitude and direction of the tension vector T3 in the third rope?
Correct: Your answer is correct. N
° (below the positive x-axis)

Answer 1

63.25 is the first part but every time I try the second I get an answer I can't work with, not sure if I'm doing the problem wrong somehow or not

Answer 2

Let t be the angle made by T3 with the x-axis.
T3 * cos(t) = 20 N ---- (1)
T3 * sin(t) = 60 N ----- (2)
Square both equations and add:
T3^2 = 20^2 + 60^2 = 400 + 3600 = 4000
T3 = sqrt(4000) = 63.25 N

divide (2) by (1):
tan(t) = 60/20 = 3
t = arctan(3) = 71.57 degrees.

Answer 3

Since the angle clockwise from the x-axis some books may call it a negative angle and say the angle is -71.57 degrees or round it to -71.6 or even -72 degrees.