Let x be the distance from the lamppost to your friend, and y the distance from the lamppost to the tip of her shadow. Then y-x is the length of her shadow, and by similar triangles,

B

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A----------C--------P

\----x-----/\-(y-x)-/

Solving for y:

For (a), we want . We use the chain rule , along with y in terms of x above and the fact that from the problem.

For (b), we remember that the shadow length is y-x, and so we want , which should follow easily from the answer to (a).

--Kevin C.