Question

1. intro to soh - cah - toa due december 14 at 8:00 pm grade: 30% pythagorean theorem (radical answers) find the length of the third side. if necessary, write in simplest radical form. score: 0/2 penalty: none question 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, the legs are \(a = 5\) and \(b = 8\), and we want to find the hypotenuse \(c\).

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

Step2: Calculate the squares

$$5^{2}=25$$

and

$$8^{2}=64$$

. So,

$$c^{2}=25 + 64=89$$

.

Step3: Solve for \(c\)

Taking the square root of both sides, \(c=\sqrt{89}\). Since 89 is a prime number, \(\sqrt{89}\) is in simplest radical form.

Answer:

\(\sqrt{89}\)