# How do you use the Pythagorean Theorem to determine if the three numbers could be the measures of the sides of a right triangle assuming that the largest is the hypotenuse: 72, 17, 19?

is true.

For this case

Plugging in, the left hand side gives

The right hand side gives

Since the equality does not hold, there is no right-angle triangle with sides measuring 17, 19 and 72.

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To determine if the three numbers 72, 17, and 19 could be the measures of the sides of a right triangle, we can use the Pythagorean Theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In this case, the largest number, 72, is assumed to be the hypotenuse. We can check if this is true by squaring the other two numbers and adding them together.

17^2 + 19^2 = 289 + 361 = 650

Now, we need to check if the square of the hypotenuse (72^2) is equal to the sum we just calculated (650).

72^2 = 5184

Since 5184 is not equal to 650, the three numbers 72, 17, and 19 cannot be the measures of the sides of a right triangle.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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