# Math Help - Statics problem

1. ## Statics problem

Can I get some help with problem 2.53 shown below?

2. let $\theta$ be the angle AB makes with the horizontal

$\phi$ be the angle BC makes with the horizontal

$T$ = wire tension

$W$ = weight of aerailist

$\sum{F_x} = 0$

$(T+35)\cos{\theta} = T\cos{\phi}$

$\sum{F_y} = 0$

$(T+35)\sin{\theta} + T\sin{\phi} = W$

let the length of $AB = x$ ... then the length of $BC = 8-x$

let $h$ = vertical distance (amount of "dip") point B is below AC

$h^2 = x^2 - 2.5^2$

$h^2 = (8-x)^2 - 5.45^2$

$(8-x)^2 - 5.45^2 = x^2 - 2.5^2$

solve for $x$, then you can determine

$\cos{\theta} = \frac{2.5}{x}$

$\cos{\phi} = \frac{5.45}{8-x}$

finally, solve your system of force equations for T and W.