Calculating Tension in Ropes for a Suspended Circus Performer

[qwertz]

Homework Statement

After a mishap, a 76.0-kg circus performer clings to a
trapeze, which is being pulled to the side by another circus
artist, as shown here. Calculate the tension in the two ropes
if the person is momentarily motionless. Include a free body diagram in your solution

Homework Equations

∑F_x = T₂cos10-T₁sin(15)=0
∑F_y=T₁cos(15)+T₂sin(10)-m*g=0

The Attempt at a Solution

Here is my free body diagram:

I am not sure are my equations valid.

 

[berkeman]

Welcome to the PF.

Looks good so far, so keep on going...

 

[qwertz]

Is it also valid if I calculate angle of T₁ as 90 - 15 = 75 and write equations as:

Σx = -T₁cos(75) + T₂cos(10) = 0
Σy =T₁sin(75) + T₂sin(10) - m*g = 0