Question

18.) a= 3√3, b= 3, c= ???

Explanation:

Assuming this is a right - triangle problem with \(a\) and \(b\) as the legs and \(c\) as the hypotenuse, we use the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\).

Step 1: Calculate \(a^{2}\) and \(b^{2}\)

Given \(a = 3\sqrt{3}\), then \(a^{2}=(3\sqrt{3})^{2}=3^{2}\times(\sqrt{3})^{2}=9\times3 = 27\).
Given \(b = 3\), then \(b^{2}=3^{2}=9\).

Step 2: Calculate \(a^{2}+b^{2}\)

\(a^{2}+b^{2}=27 + 9=36\).

Step 3: Calculate \(c\)

Since \(c=\sqrt{a^{2}+b^{2}}\) and \(a^{2}+b^{2}=36\), then \(c=\sqrt{36}=6\).

Answer:

\(c = 6\)