Question

what is the side length of a right triangle with hypotenuse 17 and one side 8?
a 19
b 18
c 15
d 16

Explanation:

Step1: Apply Pythagorean theorem

Let the hypotenuse be $c = 17$, one side be $a = 8$, and the other side be $b$. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, so $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $c = 17$ and $a = 8$ into the formula: $b=\sqrt{17^{2}-8^{2}}=\sqrt{(17 + 8)(17 - 8)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). Then $b=\sqrt{25\times9}=\sqrt{225}=15$.

Answer:

C. 15