Which set of numbers forms a right triangle? 5,12,15 8,15,19 58,156,192 60,91,109

To determine which set of numbers forms a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as:<br /><br />c² = a² + b²<br /><br />where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.<br /><br />Let's apply this to each set of numbers:<br /><br />1. For the set $5,12,15$, we can check if 15² = 5² + 12². Calculating, we find that 225 is not equal to 25 + 144, so this set does not form a right triangle.<br /><br />2. For the set $8,15,19$, we can check if 19² = 8² + 15². Calculating, we find that 361 is equal to 64 + 225, so this set does form a right triangle.<br /><br />3. For the set $58,156,192$, we can check if 192² = 58² + 156². Calculating, we find that 36864 is not equal to 3364 + 24336, so this set does not form a right triangle.<br /><br />4. For the set $60,91,109$, we can check if 109² = 60² + 91². Calculating, we find that 11881 is not equal to 3600 + 8281, so this set does not form a right triangle.<br /><br />Therefore, the set of numbers that forms a right triangle is $8,15,19$.