Solving Vectors and Forces Homework Problem

[P.townsville]

Homework Statement

A sign weighs 150n and is suspended on 2 wires between 2 walls, 1 at 50 degrees to the wall and the other at 40 deg to the other wall. What is the tension in each wire?

Homework Equations

The Attempt at a Solution

For the 1st wire F=150/cos50
=233.36N
2nd wire F=150/cos40
=195.81N
Is this likely to be correct I can't find any simular examples to help me out.

 

[tiny-tim]

Welcome to PF!

Hi P.townsville! Welcome to PF!

(have a degree: º )

A sign weighs 150n and is suspended on 2 wires between 2 walls, 1 at 50 degrees to the wall and the other at 40 deg to the other wall. What is the tension in each wire?
…
For the 1st wire F=150/cos50
=233.36N
2nd wire F=150/cos40
=195.81N

Nooo …

you're saying F₁cos50º = 150, F₂cos40º = 150.

But if you're taking vertical components, that'll be F₁cos50º + F₂cos40º = 150, won't it?

Hint: you need one equation for both vertical components, and another equation for both horizontal components, and then a bit of algebra and trig.

(Alternatively, find a direction in which you can ignore one of the tension forces )