Question

the pythagorean theorem
find the length of the leg x of the right triangle shown below.
round your answer to the nearest thousandth as needed.
question help: read

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here, let \(x\) be one leg, \(a = x\), \(b = 8\) and \(c = 17\). Then \(x^{2}+8^{2}=17^{2}\).

Step2: Rearrange the equation to solve for \(x\)

\(x^{2}=17^{2}-8^{2}\). Calculate \(17^{2}=289\) and \(8^{2}=64\). So \(x^{2}=289 - 64=225\).

Step3: Take the square - root of both sides

\(x=\sqrt{225}\). Since \(x\) represents the length of a side of a triangle, we take the positive square root. \(x = 15\) cm.

Answer:

15 cm