Q.258. Statics - equilibrium of three concurrent forces.

Question 258.
A, B are two fixed points in a horizontal line at a distance c apart. Two light strings AC and BC of length b and a respectively support a mass at C. Show that the tension of the strings are in the ratio
b(c^2+a^2 - b^2) : a(b^2+c^2 - a^2).

Answer 258.
Let T1 = tension in the string AC
and T2 = tension in the string BC
 By Lami's theorem (see link below)
http://en.wikipedia.org/wiki/Lami's_theorem

Refer to the figure as under.

T1 / sin[π - (π/2 - B)] = T2 / sin[π - (π/2 - A)]
=> T1 / cosB = T2 / cosA
=> T1 : T2
= cosB : cosA
= [(c^2 + a^2 - b^2) / (2ca)] : [(b^2 + c^2 - a^2) / (2bc)]
= b(c^2+a^2 - b^2) : a(b^2+c^2 - a^2).

Link to YA!