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, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(c = 8\), \(b=7\), and \(a=x\). So \(x^{2}+7^{2}=8^{2}\).

Step2: Simplify the equation

\(x^{2}+49 = 64\). Then \(x^{2}=64 - 49\).

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

\(x^{2}=15\).

Step4: Solve for \(x\)

\(x=\sqrt{15}\approx3.87\)

Answer:

\(3.87\)