This is a tough question. What you have to do is add some information to the diagram.
View attachment 17755
Notice that the dotted line and the solid line are parallel, therefore alternate angles are equal.
Now, imagine that you have something on the end of a string which has a force of 200 N downwards. It has to be in equilibrium. So the addition of the horizontal forces must equal 0.
However, the addition of the vertical forces must equal 200 N, as the object (which has a force of 200 N) is in equilbrium. Hence the downwards force (which is 200 N) must equal the total upwards force (T1y + T2y = 200)
So therefore:
T1x = T2x (1)
T1y + T2y = 200 (2)
Now that we have two simultaneous equations, we can use trigonometry now to form several equations.
sin 26° = T1y / T1
Therefore, T1y = T1 sin 26°
Repeat that for the rest:
sin 45° = T2y / T2
Therefore, T2y = T2sin 45°
cos 26° = T1x / T1
Therefore, T1x = T1cos 26°
cos 45° = T2x / T2
Therefore, T2x = T2cos 45°
Substitute these values into the original simulataneous equations.
T1cos 26° = T2cos 45° (1)
T1 sin 26° + T2sin 45° = 200 (2)
Therefore solve simultaneously:
T1cos 26° = 1/√2 T2
T1 sin 26° + 1/√2 T2 = 200
Therefore:
T1 sin 26° + T1cos 26° = 200
T1(sin 26° + cos 26°) = 200
Therefore T1 = 149.57 N
Now sub T1 into one of the equations to find T2
Therefore T2 = 190.12 N
