Question

find the length of the third side. if necessary, round to the nearest tenth.
answer attempt 7 out of 100
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Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 6\) and \(b = 8\), and hypotenuse \(c\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\).
Substitute \(a = 6\) and \(b = 8\) into the formula: \(6^{2}+8^{2}=c^{2}\).
Calculate \(6^{2}=36\) and \(8^{2}=64\). Then \(36 + 64=c^{2}\), so \(c^{2}=100\).

Step2: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{100}\).
Since \(c>0\) (length of a side), \(c = 10\).

Answer:

\(10\)