Question

1. $a^{2}+b^{2}=c^{2}$ $x^{2}+6^{2}=15^{2}$ $x^{2}+36=225$ $36-36$ $189$

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(c = 15\), \(b=6\), and \(a=x\). So the equation is \(x^{2}+6^{2}=15^{2}\).

Step2: Simplify the equation

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Step3: Solve for \(x\)

\(x=\sqrt{189}=\sqrt{9\times21}=3\sqrt{21}\approx13.75\)

Answer:

\(x = 3\sqrt{21}\approx13.75\)