This is a question I found in Mechanics for Engineers by Beer & Johnston.
A 600-lb crate is supported by the rope and pulley arrangement as shown below.
Write a computer program which can be used to determine, for a given value of $\beta$, the magnitude and direction of the force $F$ which should be exerted on the free end of the rope. Use this program to calculate $F$ and $\alpha$ for values of $\beta$ from 0 degrees to 30 degrees at 5 degree intervals.
For writing the program, I need to obtain a relation between $F$, $\beta$ and $\alpha$. The only thing which I was able to think of was that the component $Fcos\alpha=600 lb$ I tried to relate the angles $\alpha$ and $\beta$ by using high school geometry but I did not obtain any result which I could use.
Can anyone help me with the physics part of the question?