# math

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A woman 5 ft tall is standing near a street lamp that is 12 ft tall. Find a function that models the length L of her shadow in terms of her distance d from the base of the lamp.

• math -

This one's kind of pretty. I first thought we'd be into sin and trig country, but we don't have to. But you have to see it in a diagram.

Draw lines for the lamppost and the woman, and a line from the top of the lamppost just over the woman to the ground. You should have a big RAT, with the woman forming a similar, smaller RAT, included. Distance from lamppost to woman is d; length of shadow is s.

Key word is similar. The ratio of the sides is the same in the big and small triangles.

The base of the big triangle is s+d, and its height is 12.

The base of the small triangle is s, and its height is 5.

So we have:

(s+d)/12 = s/5

and now all you have to do is manhandle that equation to get s in terms of d!

• math -

S=5d/7

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