Calculating Tension in a Horizontal Clothesline with Vectors

[Mark Nussbaum]

For some reason I'm really struggling to get a correct answer on this problem

"A horizontal clothesline is tied between 2 poles, 20 meters apart.
When a mass of 3 kilograms is tied to the middle of the clothesline, it sags a distance of 4 meters.

What is the magnitude of the tension on the ends of the clothesline?"

Work:
Fg = 3kg*9.81m/s^2 = 29.43
found θ with arctan(4m/10m) = 21.8°
moving the origin onto the point on the forces I then used component tree to solve for the y-direction where
Ft*sin(21.8)+Ft*sin(21.8)-Fg=0,
and ignored x since they would cancel out.

the answer I got was Ft = 39.623N
when I work in reverse the magnitude gives me the correct #s and everything adds to 0.

It's been a long time since I've done this kind of physics so maybe I'm missing something dumb here. But I can't find it.

 

[Orodruin]

Seems fine to me. Why do you think there is a problem?

 

[Mark Nussbaum]

It is an online problem so it gives feedback and apparently this is an incorrect answer.

 

[Orodruin]

Some automated answer checkers will be very particular about what type of answers they accept. Minor things such as the number of decimals, the value of g that you use, or rounding errors can play a role in this.

 

[Mark Nussbaum]

Thanks I got it apparently I had to use exactly 9.8 for gravity.