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**atac777** On a morning of a day when the sin will pass directly overhead, the shadow of an 80-ft building on a level ground is 60 ft long. At the moment in question, the angle $\displaystyle \theta$ the sun makes with the ground is increasing at the rate of $\displaystyle 0.27 \deg$/min. At what rate is the shadow decreasing? (Remember to use radians and express your answer in inches per minute, to the nearest degree.)

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It's basically a triangle. y is 80, x is unknown, as is r (or z, whichever way you want to look at it).

The givens are that $\displaystyle \frac{d\theta}{dt}=0.27\deg/min$

I have to find $\displaystyle \frac{dx}{dt}$ when x = 60. It is going to be negative because the shadow length is decreasing.

My problem is that I cannot find the proper formula to go along with this equation. I've tried to use the area of a triangle, but since I don't know $\displaystyle \frac{dA}{dt}$, that gets me nowhere. I think that using trigonometric ratios is the way to go, but I keep getting mixed numbers, ranging from decimals down into the thousandths, all the way up to the thousands. The answer (according to the book) is 7.1 in/min.

Solving the problem is not necessary. If you can help me find the right formula, I can take it from there.

I thank you for your time if you chose to post here.