Question

1. intro to soh - cah - toa due: december 14 at 8:00 pm grade: 30% pythagorean theorem (radical answers) score: 0/2 penalty: none question find the length of the third side. if necessary, write in simplest radical form. identifying trig ratios (diagram), level 1 identifying trig ratios (diagram), level 2 identifying trig ratios (diagram), level 2 identifying trig ratios (diagram), level 1 angles (algebraic) pythagorean theorem (radical answers) back to home answer attempt 2 out of 2 watch video start example submit answer deltamath

Explanation:

Step1: Recall Pythagorean theorem

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

$$8^{2}=64$$

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

$$c^{2}=89$$

Step3: Solve for \(c\)

Take the square root of both sides. Since \(c>0\) (as it represents the length of a side of a triangle), \(c=\sqrt{89}\).

Answer:

\(\sqrt{89}\)