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12 December, 05:03

Antonio is a biologist studying life in a pond. He needs to know how deep the water is. He notices a water lily sticking straight up from the water, whose blossom is 8 cm above the water's surface. Antonio pulls the lily to one side, keeping the stem straight, until the blossom touches the water at a spot 40 cm from where the stem first broke the water's surface. How is Antonio able to calculate the depth of the water? What is the depth?

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  1. 12 December, 05:14
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    For this problem we can represent the situation as a rectangle triangle.

    x: depth of water.

    40: Base. "Antonio pulls the lily to one side, keeping the stem straight, until the blossom touches the water at a spot"

    x + 8: Hypotenuse. "He notices water lily sticking straight up from the water, whose blossom is 8 cm above the water's surface." Antonio pulls the lily to one side, keeping the stem straight, until the blossom touches the water at a spot".

    By the Pythagorean theorem we have:

    x ^ 2 + 40 ^ 2 = (x + 8) ^ 2

    Clearing x:

    x ^ 2 + 1600 = x ^ 2 + 16x + 64

    x ^ 2 - x ^ 2 = 16x + 64 - 1600

    0 = 16x - 1536

    1536 = 16x

    1536/16 = x

    x = 96

    answer:

    1) x ^ 2 + 40 ^ 2 = (x + 8) ^ 2

    2) the depth of the water is

    x = 96
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