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, \(c = 12\), \(a=x\), \(b = 11\). So \(x^{2}+11^{2}=12^{2}\).

Step2: Simplify the equation

\(x^{2}+121 = 144\). Then \(x^{2}=144 - 121\).

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

\(x^{2}=23\).

Step4: Solve for \(x\)

\(x=\sqrt{23}\approx4.7958\). Rounding to the nearest hundredth, \(x\approx4.80\).

Answer:

\(4.80\)