Question

question find the length of the third side. if necessary, write in simplest radical form. score: 0/2 penalty: none pythagorean theorem (radical answers) answer attempt 1 out of 2

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here \(a = 5\), \(b = 8\), and we want to find \(c\).

$$c^{2}=5^{2}+8^{2}$$

Step2: Calculate the squares

$$5^{2}=25$$

and

$$8^{2}=64$$

. So \(c^{2}=25 + 64=89\).

Step3: Solve for \(c\)

$$c=\sqrt{89}$$

Answer:

\(\sqrt{89}\)