[WWfeedback] course:Taylor_MAT_267_Fall_2015:Section_10.2 prob:11

Hi Dr Taylor,
I've worked through this one a few times and get the same
answer. I've tried giving WebWork answers with greater precision with no
joy.

Let T be the tension in the clothesline.
Then 2T cos Ɵ = m.g

The angle is arctan(1/7) = 8.1301°
Then 2T = (4 * 9.8) / cos(8.1301°)
2T =39.598 N
Then T = 19.799 N

Am I missing something?

First of all, for everybody's benefit here is a link to my discussion of this problem a year ago.  Your equation 2T cos Ɵ = m.g follows from the idea that the sum of the two tensions should balance the force of gravity, hence be vertical, and that the sum is twice the vertical component of either tension.  The magnitude of both vertical components is T cos Ɵ where  Ɵ is the angle formed between the rope and the vertical direction.  Eye-balling it suggests that this should be quite a bit larger than the 8.1301°, so I think you have the wrong angle...and in fact the opposite of this angle is 7m and the adjacent is 1m, so you should have had the formula Ɵ=arctan(7)=1.429rad=81.89°.
Then 2T = (4 * 9.8) / cos(81.89°)=277.19 etc.