A person is standing on tiptoe, with the total weight supported by the force on the toe. A mechanical model for the situation is shown, where T is the force in the Achilles tendon and R is the force on the foot due to the tibia. Find the value of T. Assume the total weight is 484N. Answer in units of N.
R = unknown
T = unknown
Distance of T from point of rotation = 32cm = l2
Distance of R from point of rotation = 30.29cm = l1
Angle of T with respect to force acting at point of rotation = 21.2 degrees = θ
Angle of R with respect to force acting of point of rotation = 14.4 degrees = φ
It's a statics problem, so there's no rotational or translational motion. Also, the forces are orthogonal to the radial axis.
The Attempt at a Solution
Since there are only two unknowns, I took the relationship between the two torques to find R in terms of T, R=T(l2/l1). I then plugged this into the equation for the sum of forces in the y-direction, and I got the answer 672.5992756N for T, but this apparently isn't correct. I really can't figure out what I'm doing wrong, so any help would be appreciated.