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?

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