Question

what is the length of the hypotenuse in a right triangle with legs of length 14 and 48?

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here \(a = 14\) and \(b = 48\). So we have \(c^{2}=14^{2}+48^{2}\).

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Step2: Solve for \(c\)

Take the square root of both sides. Since \(c>0\) (length), \(c=\sqrt{2500}\).

$$c = 50$$

Answer:

\(50\)