Question

find the length of the hypotenuse, c, for the right triangle with sides, a = 3 and b = 4.
c =
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Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a = 3\), \(b = 4\).
So, \(3^{2}+4^{2}=c^{2}\).

Step2: Calculate \(a^{2}\) and \(b^{2}\)

\(3^{2}=9\), \(4^{2}=16\).
Then \(9 + 16=c^{2}\), i.e., \(c^{2}=25\).

Step3: Solve for \(c\)

Take the square root of both sides. Since \(c>0\) (length of a side), \(c=\sqrt{25}\).

Answer:

\(5\)