Question

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

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a = 8\), \(b = 10\), and \(c=x\).
So, \(x^{2}=8^{2}+10^{2}\).

Step2: Calculate \(8^{2}+10^{2}\)

\(8^{2}=64\) and \(10^{2}=100\). Then \(8^{2}+10^{2}=64 + 100=164\).
So, \(x^{2}=164\).

Step3: Solve for \(x\)

\(x=\sqrt{164}\).
Since \(\sqrt{164}=\sqrt{4\times41}=2\sqrt{41}\approx 12.81\) (using a calculator to find \(\sqrt{41}\approx6.403\) and \(2\times6.403 = 12.806\approx12.81\)).

Answer:

\(12.81\)