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 \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here, \(c = 20\), \(a = 11\), and \(b=x\). So, \(x^{2}+11^{2}=20^{2}\).

Step2: Rearrange the equation

We can rewrite the equation as \(x^{2}=20^{2}-11^{2}\). Calculate \(20^{2}=400\) and \(11^{2}=121\). Then \(x^{2}=400 - 121=279\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{279}\approx16.70\).

Answer:

\(16.70\)