A student is asked to find the length of the hypotenuse of a right triangle. The length of one leg is 30 cm, and the length of the other leg is 26 cm. The student incorrectly says that the length of the hypotenuse is 7.5 cm. Find the length of the hypotenuse of a right triangle to the nearest 10th of a centimeter
Accepted Solution
A:
Answer: The length of the hypotenuse ≈ 39.7 cm
Explanation: Since the given triangle is a right-angled triangle, this means that we can apply the Pythagorean theorem. The equation for Pythagorean calculation is: (hypotenuse)² = (first leg)² + (second leg)²
In the given, we have: first leg = 30 cm second leg = 26 cm
Substitute with the givens in the above equation to get the hypotenuse as follows: (hypotenuse)² = (30)² + (26)² (hypotenuse)² = 1576 This means that: either hypotenuse = √1576 = 39.69 ≈ 39.7 cm ..........> accepted or hypotenuse = -√1576 = -39.69 ......> rejected as length can't be negative