Question

for the following right triangle, find the side length x. round your answer to the nearest hundredth.

Explanation:

Step1: Apply Pythagorean theorem

$$a^{2}+b^{2}=c^{2}$$, where \(c = 17\), \(a=10\), \(b = x\). So \(x^{2}+10^{2}=17^{2}\).

Step2: Solve for \(x^{2}\)

\(x^{2}=17^{2}-10^{2}\). Calculate \(17^{2}=289\), \(10^{2} = 100\). Then \(x^{2}=289 - 100=189\).

Step3: Find \(x\)

\(x=\sqrt{189}\approx13.75\)

Answer:

\(13.75\)