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December 22, 2014

December 22, 2014

Posted by **Amy** on Saturday, February 12, 2011 at 9:24am.

I know that this forms a right triangle with a hypotenuse of 15 an two legs that measure 9 (for x) and 12 (for y).

My first step was:

x dx/dt + y dy/dt = z dz/dt

9(5) + 12 dy/dt = 15(0)

dy/dt = 3.75 ft/sec

Then I attempted to answer the second part of the question, but I wasn't sure how to do this.

What I did was:

A=1/2bh or 1/2xy

dA/dt = 1/2 x dy/dt + 1/2 y dx/dt

dA/dt = 1/2(9)(3.75) + 1/2(-12)(5)

dA/dt = -105/8 ft^2/sec

-------> I'm not sure if this is the right process or if I'm supposed to be looking for an angle? Any help is appreciated, thanks

- Calculus - not sure if my work is correct? -
**Reiny**, Saturday, February 12, 2011 at 9:40amYour first part is correct, except your

dy/dt should be -3.75 (showing that is slides "down")

for your second part , since we are involving an angle, we have to introduce an equation containing an angle.

Trig will do this.

So let the base angle be Ų

cosŲ = x/15

15cosŲ = x

-15sinŲ dŲ/dt = dx/dt

for our given case, sinŲ = 12/15 = 4/5

dŲ/dt = -5/(15(4/5)) = -5/12 radians per

The negative says that the angle is decreasing, which makes sense as the ladder is falling.

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