# Thread: help with a related rate problem

1. ## help with a related rate problem

On a sunny and cold morning , the sun will pass directly overhead of an 80 ft building. At noon( before the sun passes directly over the building) ,the sun casts a 60 ft shadow on level ground and the angle the sun makes with the grund, A, is increasing at the rate of 0.27 degrees per minute.

At noon

a) At what rate is the shadow decreasing?

b)How fast is the distance from the top of the building to the end of the shadow changing ( it's getting shorter)

I know I'm given a rate , which is dA/dt = 0.27 degrees / minute ; however, my instructor only covered related rates briefly .Can someone help me with this problem? thanks in advance

2. Related rates nearly always depend on the chain rule, so you might want to try filling up this pattern...

... where straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in this case time), and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

Here, the two variables to relate are the angle A and shadow length x...

So differentiate with respect to the inner function, and the inner function with respect to t, and sub in the given values of x and dA/dt...

Spoiler:

__________________________________________

Don't integrate - balloontegrate!

Balloon Calculus: Gallery

Balloon Calculus Drawing with LaTeX and Asymptote!

3. Thanks for your help Tom ; however, I'm not supposed to use either csc or cot to work on this problem ( I'm only taking my first calculus course, so I haven't covered that yet). Thanks though. Can someone show me how to do it a little more simpler?

4. Yes, you could say...

__________________________________________

Don't integrate - balloontegrate!

Balloon Calculus: Standard Integrals, Derivatives and Methods

Balloon Calculus Drawing with LaTeX and Asymptote!

5. thanks , I got it!!!