Question

question
find the length of the third side. if necessary, round to the nearest tenth.
(there is a right triangle with legs 6 and 8, and the right angle between them, and we need to find the hypotenuse or the other side? wait, no, in the triangle, one leg is 6, the other leg? wait, the triangle has a right angle, one side is 6, another is 8? wait, the ocr text: the image shows a right triangle with one leg 6, the hypotenuse? wait, no, the problem is to find the length of the third side. so the triangle is right-angled, with two sides given: 6 and 8, and we need to find the third. so using pythagorean theorem. so ocr text: \question find the length of the third side. if necessary, round to the nearest tenth.\ and the image is a right triangle with legs 6 and 8? wait, no, in the image, the triangle has a right angle, one side is 6, another is 8? wait, the ocr text after extracting: the problem is to find the third side of a right triangle with two sides (6 and 8) given, right-angled. so ocrtext is: \question find the length of the third side. if necessary, round to the nearest tenth.\

Explanation:

Step1: Identify triangle type

It's a right - triangle (has a right - angle symbol). Let the two legs be \(a = 6\) and \(b = 8\), and the hypotenuse be \(c\).

Step2: Apply Pythagorean theorem

The Pythagorean theorem states that for a right - triangle, \(c^{2}=a^{2}+b^{2}\). Substitute \(a = 6\) and \(b = 8\) into the formula:
\(c^{2}=6^{2}+8^{2}=36 + 64=100\)

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{100} = 10.0\) (rounded to the nearest tenth)

Answer:

\(10.0\)