Question

square roots and the pythagorean theore vectored instruction find the length of “a”using the pythagorean theorem.

Explanation:

Step1: Recall Pythagorean Theorem

The Pythagorean Theorem for a right - triangle is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(c = 15\), \(b = 9\), and we want to find \(a\). So, \(a^{2}+9^{2}=15^{2}\).

Step2: Simplify the equation

First, calculate \(9^{2}=81\) and \(15^{2}=225\). The equation becomes \(a^{2}+81 = 225\). Then, subtract 81 from both sides: \(a^{2}=225 - 81\).

Step3: Calculate the right - hand side

\(225-81 = 144\), so \(a^{2}=144\).

Step4: Solve for \(a\)

Take the square root of both sides. Since \(a\) represents the length of a side of a triangle, we take the positive square root. \(a=\sqrt{144}=12\).

Answer:

12