Finding cable tension for a suspended speaker

[pemby]

1. The problem statement, all variables, and given/known data

Homework Equations

Assuming standard coordinates, Net forces in the x plane are 0, by

The Attempt at a Solution

I have worked out that

$$\arcsin { \left( \frac { 1.4 }{ 3.1 } \right) } =\quad 26.8{ 5 }°\\ loud\quad speaker\quad =\quad wg\quad =\quad 166.77\quad N\\ 2T\sin { \left( 26.8{ 5 }° \right) \quad =\quad 166.77 } N\\ T\quad =\quad 84.2824$$

Masteringphysics returning with an incorrect solution response and is giving me this piece of information.

I do not understand what this error implies.
I have tried;

$$\\ T\sin { \left( 26.8{ 5 }° \right) \quad =\quad 166.77 } N\\ \\ \\ T\sin { \left( \frac { 1 }{ 2 } 26.8{ 5 }° \right) \quad =\quad 166.77 } N\\ \\ T2\sin { \left( 26.8{ 5 }° \right) \quad =\quad \frac { 166.77\quad N }{ 2 } }$$

 

[haruspex]

Radians v. degrees.

 

[pemby]

Sorry, can you expand a bit more? I understand the difference but not in the context of this question.

 

[haruspex]

sin(26.85°)

What value did you get for that?

 

[pemby]

What value did you get for that?

0.438371146789077417452734540658265739062755719988552114431

 

[haruspex]

0.438371146789077417452734540658265739062755719988552114431

Then I do not see how you could have got that final answer. You had

2Tsin(26.85°)=166.77N

Maybe you halved twice?

 

[pemby]

https://www.wolframalpha.com/input/?i=2*y*sin(26.85)+=+166.77

 

[pemby]

Thanks. it was reading my degrees as radians. I tricked my self by not double checking!

 

[haruspex]

Thanks. it was reading my degrees as radians. I tricked my self by not double checking!

OK.

Btw, you can often avoid figuring out the angle. In the present case, you wanted sin(θ), which is h/l, so the accurate answer is 17g*3.1/(2*1.4).