Question

question
find the length of the third side. if necessary, round to the nearest tenth.
answer attempt 2 out of 2

Explanation:

Step1: Identify triangle type

It's a right triangle, so use Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(c\) is hypotenuse, \(a,b\) legs. Here, legs are 6 and 8, hypotenuse? Wait, no—wait, the side labeled 8 is hypotenuse? Wait, no, the right angle is between the two legs, so the side opposite right angle is hypotenuse. Wait, the triangle has right angle, one leg 6, hypotenuse? Wait, no, the side with length 8 is the hypotenuse? Wait, no, maybe I misread. Wait, the triangle: right angle, one leg 6, another leg? Wait, no, the problem is to find the third side. Wait, maybe the two legs are 6 and \(x\), hypotenuse 8? Wait, no, let's check. Wait, Pythagorean theorem: if it's a right triangle, then \(a^2 + b^2 = c^2\). Let's see: if the two legs are 6 and \(x\), hypotenuse 8? Wait, no, 6² + x² = 8²? Wait, no, maybe the hypotenuse is the third side. Wait, the given sides: one leg 6, another leg? Wait, the diagram: right angle, one leg 6, the other leg? Wait, no, the side labeled 8 is the hypotenuse? Wait, no, maybe the two legs are 6 and \(x\), and the hypotenuse is 8? Wait, no, 6² + x² = 8² → x² = 64 - 36 = 28 → x = √28 ≈ 5.3? No, that can't be. Wait, maybe I got the sides wrong. Wait, maybe the legs are 6 and 8, hypotenuse is the third side. Wait, 6² + 8² = c² → 36 + 64 = c² → 100 = c² → c = 10. Oh! Wait, that makes sense. So the third side (hypotenuse) is 10.

Step2: Apply Pythagorean theorem

Let \(a = 6\), \(b = 8\), find \(c\).
\(c^2 = 6^2 + 8^2\)
\(c^2 = 36 + 64\)
\(c^2 = 100\)
\(c = \sqrt{100} = 10\)

Answer:

10