Posted by **Anonymous** on Friday, November 16, 2012 at 1:20pm.

A 12' ladder is leaning against a wall making an angle theta with the ground. The ladder begins to slide down the wall. what is the rate of change of the height of the ladder, h, with respect to the change in the angle of the ladder with the floor when the ladder reaches a height of 9 feet?

- Calculus -
**Steve**, Friday, November 16, 2012 at 2:51pm
if the distance from wall is x,

x^2 + h^2 = 144

x = √(144-h^2)

when h=9, x = √(144-81) = √63

sinθ = h/12

the wording of the question is odd. Usually they ask for the rate of change of x when h=9. In that case,

2x dx/dt + 2h dh/dt = 0

but we don't have dh/dt.

So, it appears they want dh/dθ

h/12 = sinθ

h = 12sinθ

dh/dθ = 12cosθ = 12(x/12) = x = √63

however, rather than asking for "the rate of change of h with respect to θ" you say they want "rate of change of h with respect to the change of θ". Don't know how to interpret that

## Answer This Question

## Related Questions

- CALCULUS - A 25 ft ladder is leaning against a vertical wall. At what rate (with...
- maths - a 4m ladder is leaning against a wall when its base starts to slide ...
- Calculus Ladder Problem - A ladder 20 ft long rests against a vertical wall. Let...
- Calculus - related rates: a ladder, 12 feet long, is leaning against a wall. if ...
- calculus - A ladder 14 ft long rests against a vertical wall. Let \theta be the ...
- Calculus - 1a. 15 ft ladder is placed against a vertical wall. the bottom of the...
- math - A ladder 14 ft long rests against a vertical wall. Let \theta be the ...
- Math - A ladder 20 ft long rests against a vertical wall. Let \theta be the ...
- Math - A ladder 20 ft long rests against a vertical wall. Let \theta be the ...
- Math - A ladder is leaning up against a wall. The ladder touched the wall 5ft up...

More Related Questions