Math Help - Relate Rates Problem

1. Relate Rates Problem

Here is the question I am having trouble with:
The sun is passing over a 100 m tall building. The angle θ made by the sun with the ground is increasing at a rate of pi/20 rads/min. At what rate is the length of the shadow of the building changing when the shadow is 60 m long? Give your answer in exact values.
So far I have got:
100cosfata=x

dx/dt=-100(cosfata)(dfata/dx)
Dont no where to get cosfata from.

2. Re: Relate Rates Problem

"Increasing at a rate of rads/min?"

3. Re: Relate Rates Problem

Oh my gosh I have read this problem so many times I can just picture the numbers when they are not even there. Ugh.

4. Re: Relate Rates Problem

The sun is passing over a 100 m tall building. The angle θ made by the sun with the ground is increasing at a rate of pi/20 rads/min. At what rate is the length of the shadow of the building changing when the shadow is 60 m long?
$\cot{\theta} = \frac{x}{100}$

$-\csc^2{\theta} \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot \frac{dx}{dt}$

5. Re: Relate Rates Problem

But how do I find a value for -csc^2fata

6. Re: Relate Rates Problem

Originally Posted by mjo
But how do I find a value for -csc^2fata
review your basic right triangle trig ...

$\csc{\theta} = \frac{hypotenuse}{opposite} = \frac{\sqrt{60^2+100^2}}{100}$

square the result and change its sign to get the value of
$-\csc^2{\theta}$

btw ... $\theta$ is prounounced "theta" , not "fata"

7. Re: Relate Rates Problem

I found my original problem. Thanks guys