Tension in two wires at 50° and 45° supporting a picture

[oceanflavored]

Tensions in Wires :)

Homework Statement

A 10.0-kg picture is held in place by two wires, one hanging at 50.0^o to the left of the vertical and the other at 45.0^o to the right of the vertical. What is the tension in the first wire? What is the tension in the second wire?

Homework Equations

Force = mass(acceleration)
Weight = mass(gravity)

The Attempt at a Solution

So, I drew my free body diagram, drawing the two forces and the weight pointing downwards in a vertical direction.
Then, I reasoned that since it was being "held in place," acceleration would be zero, meaning the net force would be zero.
so then, I tried to solve for the tension in wire that was hanging at 50.0^o to the left of the vertical:
net force = T₁ cos 50^o - (10.0 kg)(9.81 m/s²) = 0
But that gave me an answer of 152.6 N, which definitely did NOT match the book's answer of 69.6 N.

I'm sorry I'm this confused; all the previous examples/problems I've done had the wires hanging at equal angles, so the tensions were always equal :/
Thus, I'd really appreciate if you could tell me where I'm going wrong! Thank you so so so so so so much :)

 

[mgb_phys]

You have two wires - the total weight is on both of them - you have assigned all 10kg to one wire and got an answer roughly twice as large as you should

 

[oceanflavored]

So, are you telling me to divide my answer by 2?
Because, in that case, the answer for both wires would be the same??
Except, my book has different answers for each wire: 69.6 N for the first one, 75.4 N for the second.

I'm sorry; I'm still confused :/

 

[mgb_phys]

The sum of the vertical components on the wires is 10g you can use this to find the absolute tension in each wire.