A ladder 13 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft. per second,how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 5ft from the wall?

Answer 1

h is height
x is distance from wall

sin T = h/13

cos T = x/13

d cos T /dt = - sin T dT/dt =(1/13)dx/dt
or
dT/dt = -(1/(13 sin T))(dx/dt)
sin t = h/13
at x = 5
h = sqrt (169 - 25) = 12
so
sin T = 12/13
so
dT/dt = -(1/12)dx/dt = -1/12
radians/second