Question

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

Explanation:

Step1: Apply the Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(a = 15\), \(c=25\), and \(b=x\). So, \(x^{2}+15^{2}=25^{2}\).

Step2: Rearrange the formula to solve for \(x\)

\(x^{2}=25^{2}-15^{2}\).
Using the formula \(a^{2}-b^{2}=(a + b)(a - b)\), we have \(x^{2}=(25 + 15)(25-15)\).
\(x^{2}=(40)\times(10)=400\).

Step3: Calculate \(x\)

\(x=\sqrt{400 - 225}=\sqrt{175}\approx13.23\)

Answer:

\(13.23\)