Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\). Here, \(a = 8\), \(b=x\), \(c = 13\). So, \(8^{2}+x^{2}=13^{2}\).

Step2: Simplify the equation

\(64+x^{2}=169\). Then, \(x^{2}=169 - 64\).

Step3: Calculate \(x^{2}\)

\(x^{2}=105\).

Step4: Solve for \(x\)

\(x=\sqrt{105}\approx10.25\)

Answer:

\(10.25\)