Ben is a safety inspector for a family gym. Recently, guests have been complaining about the diving board saying that it is leaning towards the water. Ben needs to know whether this diving board is standing up straight or not. Ben measures the height of the diving board to be 15 feet. The pool is 13 feet across and he measures the diagonal from the other side of the pool to the top of the diving board to be 21 feet. Is the diving board at a 90 degree angle with the ground? Explain how you know.

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anonymous · Answer

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anonymous · Answer

First of all, this question is unrealistic and rather stupid -- nobody would do all these measurements to figure out if the diving board is leaning or not, for example because measurement of the diagonal (and it's wrong to call it that, but nvm) would be anything but easy. A levelling tool would suffice.

Now off to solve this "problem". :D We have lengths of three sides of a triangle formed by the bottom of the board, top of the board and the pool surface. We know from the Pythagorean theorem, that in a right triangle the following relationship holds:

$$a^2 + b^2 = c^2$$

Where 'c' is the diagonal. Your task is to check if this equation is true in this case. Good luck!