In the toggle joint of Problem assume that a and b are equal and θ = 160°. What force P is...

In the toggle joint of Problem assume that a and b are equal and θ = 160°. What force P is required to balance a force of 100 lb at F?

Problem

A toggle joint is a mechanism by which a comparatively small force P produces or balances a force F that increases rapidly as the angle θ approaches 180°. For a given angle of θ, the toggle joint becomes equivalent to a simple truss. Force P = 10 lb, a = 2 ft, b = 5 ft, and c = 1 ft, as shown. Find force F. Neglect friction and the weights of the members.