To find: The function that models the length of shadow of woman standing near a street lamp in terms of her distance from the base of the lamp.
The function that models in terms of is .
The geometric figure of the situation is shown below,
In triangle AOB as shown in Figure (1), OA is height of street lamp, CD is height of woman, L is the length of shadow of woman and d is the distance of woman from base of street lamp.
Height of woman is . and height of street lamp is
Triangles and are similar and corresponding sides of similar triangles are in same proportion.
Substitute 5 for CD, 12 for AO, L for BD and BO for in above equation.
Subtract from both the sides of above equation.
Thus, the function that models in terms of is .
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