A ladder 15 m long leans against the wall. The ladder slides down the wall at a rate of 1.5 m/s. What is the rate of change of the angle at the ground when the ladder is 6 m from the wall?

Question

a² + b² = c²

2aa + 2bb = 2cc

a = cc - bb/a = -bb/a

= - (1.5)(6) / 12√1.5

= - 9 / 12√1.5

= -0.612 ft/min

this is what i got, am i correct?

Answer 1

The question asks for the rate of change of the angle at the ground, rather than the rate of change of the other leg of the right triangle. So we should proceed instead as follows:

sinΘ = y/15

cosΘ·dΘ/dt = 1/15·dy/dt

2/5·dΘ/dt = 1/15·(-6)

dΘ/dt = - 1 radians/sec