A ladder 20 ft long is leaning against an embankment inclined 60 degrees to the horizontal. If the bottom of the ladder is being moved horizontally toward the embankment at 1 ft/sec, how fast is the top of the ladder moving when the bottom is 4 ft from the embankment?

Answer 1

from the triangle:
20^2=h^2 + x^2
h is vertical height, and x is distance base.
take the derivative...
0=2h dh/dt + 2x dx/dt

dh/dt=-dx/dt x/h
= 1 * 4/h where h= sqrt(400-16)