Question

find the value of c. use the pythagorean theorem to help you.start by substituting the value of a in the pythagorean theorem equation.the pythagorean theorem says that if a, b, and c are the sides of a right triangle, where c is the hypotenuse, then: $a^{2}+b^{2}=c^{2}$

Explanation:

Step1: Substitute the value of \(a\)

Given \(a = 6\), substitute into \(a^{2}+b^{2}=c^{2}\). So we have \(6^{2}+b^{2}=c^{2}\).

Step2: Substitute the value of \(b\)

Given \(b = 3\), substitute into the equation. Now the equation is \(6^{2}+3^{2}=c^{2}\).
Calculate \(6^{2}=36\) and \(3^{2}=9\). Then \(36 + 9=c^{2}\), so \(c^{2}=45\).

Step3: Solve for \(c\)

Since \(c^{2}=45\), then \(c=\sqrt{45}\). Simplify \(\sqrt{45}=\sqrt{9\times5}=3\sqrt{5}\approx 6.71\) (rounded to two decimal places).

Answer:

\(c = 3\sqrt{5}\approx6.71\)