s. The length of one leg of a right triangle is 5 centimeters shorter than the hypotenuse. The hypotenuse is 15 centimeters. What is the length of the unknown leg of the right triangle rounded to the nearest tenth?
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To find the length of the unknown leg of the right triangle, we start with the information given. The hypotenuse is 15 cm, and one leg is 5 cm shorter than the hypotenuse. So, the length of that leg would be 15 cm - 5 cm = 10 cm. Now, we can use the Pythagorean theorem, which states that for a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the legs (a and b): c² = a² + b². Using our values: 15² = 10² + b². This gives us 225 = 100 + b². Rearranging gives b² = 225 - 100 = 125. To find b, we take the square root, yielding b = √125, which is approximately 11.2 cm when rounded to the nearest tenth. Thus, the length of the unknown leg of the right triangle is about 11.2 centimeters.