Slidding ladder calculous problem

A 25 ft ladder is leaning against a house when its base starts to slide away. By the time the base is 7 ft from the house, the base is moving away at the rate of 24 ft/sec

**a.** what is the rate of change of the height of the top of the ladder?

**b.** at what rate is the area of the triangle formed by the ladder, wall, and ground changing then?

**c.** at what rate is the angle between the ladder and the ground changing then?

Re: Slidding ladder calculous problem

Denote the base and height of the ladder by b and h, such that $\displaystyle b^2 + h^2 = 25^2$. Differentiating both sides with respect to t,

$\displaystyle 2b \frac{db}{dt} + 2h \frac{dh}{dt} = 0$

For part a, you already know what db/dt is, as well as b and h at this moment in time. Here it is easy to find dh/dt.