Solve for the sum of 3 cable forces on one anchor point

[aatari]

Homework Statement

I solved this problem using two methods and my answer for the angle (Fr) is different for each solution. I am trying to figure out what I am doing wrong but I am stuck.

I know solution 2 is correct but why am I getting the incorrect angle when I use the sine law in sol1.

Please see attached for my work; any feedback will be greatly appreciated.

Relevant Equations

A/sina = B/sinb = C/sinc

 

[haruspex]

What solutions are there to $\sin(\theta)=x$?

 

[Lnewqban]

Your calculation of $\theta_1$ is not correct; its value should be 115.74°.

 

[haruspex]

Your calculation of $theta_1$ is not correct; its value should be 115.74°.

See post #2.

 

[aatari]

Your calculation of $\theta_1$ is not correct; its value should be 115.74°.

Could you kindly explain how? When I plug the values in my calculator I get 64.27.

 

[haruspex]

Could you kindly explain how? When I plug the values in my calculator I get 64.27.

See post #2.

 

[Lnewqban]

Could you kindly explain how? When I plug the values in my calculator I get 64.27.

I am unable to explain how mathematically.
Please, see attachment, which may help you find the error.