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Solution

Again we are employing the principles of equilibrium to solve this problem. We know that for this ladder system to be in equilibrium that the net torque must be zero. Therefore, using the bottom of the ladder as a pivot point, we'll solve the net torque equation for the weight of the man and then convert his weight to his mass. First, let's get the values for all of the lever arms that we will need for the torque formulas.

Fa Lever Arm: (Sin65)(4.6 m) = 4.2 m
Fgladder Lever Arm: (Cos65)(2.3 m) = 0.97 m
Fgman Lever Arm: (Cos65)(3.6 m) = 1.5 m

Now stick everything in the formula:

Torque CW = Torque CCW
(Fgman)(1.5 m) + (45 N)(0.97 m) = (400 N)(4.2 m)
(Fgman)(1.5 m) + (43.7 N*m) = 1667.6 N*m
(Fgman)(1.5 m) = 1623.9 N*m
Fgman = 1068

Now that we know his weight, we can easily find his mass in kg by dividing by 9.8.

Mass of man = 110 kg