Understanding x(θ) and h(θ) in a Triangle Support Beam Problem

[pyroknife]

Homework Statement

I have attached the problem. I am confused about how they got x(θ) and h(θ). From the diagram it looks like they made it with reference to the triangular support beam. Why?

Homework Equations

The Attempt at a Solution

 

[Spinnor]

This is late and my be of no use. You wrote,

From the diagram it looks like they made it with reference to the triangular support beam. Why?

It is a reference point that doesn't move? h(θ) is pretty straight forward, and if you set θ = 0 , x(0) = 3b/2 makes sense.

 

[gnulinger]

Homework Statement

I have attached the problem. I am confused about how they got x(θ) and h(θ). From the diagram it looks like they made it with reference to the triangular support beam. Why?

The length of one rod is b. b/2 at angle θ coincides with the vertical position that you want to use to define h(θ). From basic trig, h/(b/2) = sin(θ). Thus h(θ) = b/2*sin(θ).


Similarly x coincides with the horizontal position that the 1 + 1/2 rods make at angle θ. So then x = b*cos(θ) + 1/2*b*cos(θ) = 3b/2*cos(θ).