Rod and cord problem

Here's a link to the code Mathjax of the quadratic equation

The solution of the problem step by step is as follows

a)

b)

$$\begin{array}{rl}\Sigma F_x=0=& -Fhx+Tx=0\\ & Tx=Fhx\\ & Fhx=sin(\beta )·T\end{array}$$

1. In the first step we make the equation summation of forces on the horitzontal axis
2. In the second step we isolate the hinge force in the horitzontal axis
3. In the third step we substitute the horitzontal component of the tension by the data we know by trigonometry

Please enter the following data to calculate the previous equation

Enter β Enter tension

Equation 1 result is

Comment:

$$\begin{array}{rl}\Sigma F_y=0=& Ty-Fhy-W-mg=0\\ & Ty-W-mg=Fhy\\ & Fhy=T\ast cos(\beta )-W-mg\end{array}$$ In the first step we make the equation summation of forces on the vertical axis In the second step we isolate the hinge force in the vertical axis In the third step we substitute the vertical component of the tension by the data we know by trigonometry Please enter the following data to calculate the previous equation Enter β Enter tension Enter weight Enter mass Enter gravity Equation 2 result is Comment: $$\begin{array}{rl}Fh=& \surd (Fhx+Fhy)\end{array}$$ In this step, we calculate the module of Fh, using Fhx and Fhy from the previous equations. Please enter the following data to calculate the previous equation Enter Fhx Enter Fhy Equation 3 result is Comment: