Question

A woman 6 ft tall is standing near a street lamp that is 13 ft tall, as shown in the figure. Find a function that models the length L of her shadow in terms of her distance d from the base of the lamp.

Answer 1

Explanation:

We can use similar triangles to find the function that models the length of the woman's shadow. If the woman is standing at a distance d from the base of the lamp, the length of her shadow will be proportional to her height, so the ratio of the shadow length to the height will be equal to the ratio of the distance from the base of the lamp to the height of the lamp.

So, if h is the woman's height and L is the length of her shadow, we have:

L/h = d/13

And since h = 6 feet, we can write:

L = (d/13) * 6

So the function that models the length of the woman's shadow in terms of her distance from the base of the lamp is:

L = (d/13) * 6