Question

find the length of the third side. if necessary, write in simplest radical form. answer attempt 1 out of 2 pythagorean theorem (radical) finding angles in transversal problems (level 2) unit 1 test retake p6 december 9 at 3:30 pm grade 45%

Explanation:

Step1: Apply Pythagorean theorem

Let the two - known sides of the right - triangle be $a = \sqrt{39}$ and $b = 8$. The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$ for the hypotenuse $c$, or $a^{2}=c^{2}-b^{2}$ or $b^{2}=c^{2}-a^{2}$ depending on which side is the hypotenuse. Here, we assume the hypotenuse is the unknown side $c$. Then $c^{2}=(\sqrt{39})^{2}+8^{2}$.

Step2: Calculate the squares

$(\sqrt{39})^{2}=39$ and $8^{2}=64$. So $c^{2}=39 + 64$.

Step3: Sum the values

$c^{2}=39+64=103$.

Step4: Find the square - root

$c=\sqrt{103}$.

Answer:

$\sqrt{103}$