Question

fill in the missing values to find the missing value of the triangle.
$a^2 + b^2 = c^2$
$4^2 + 3^2 = c^2$
$16 + \square = c^2$
$25 = c^2$
$\square = c$

Explanation:

Step1: Calculate \(3^2\)

We know that \(b = 3\) in the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). So we calculate \(3^{2}\), and \(3^{2}=9\). So the first missing value (in the box under \(16 + \square=c^{2}\)) is \(9\) since \(4^{2}=16\) and \(3^{2} = 9\), so \(16+9=c^{2}\).

Step2: Solve for \(c\) when \(25 = c^{2}\)

We have the equation \(25=c^{2}\). To find \(c\), we take the square root of both sides. The square root of \(25\) is \(5\) because \(5\times5 = 25\). So the second missing value (in the box under \(25 = c^{2}\)) is \(5\) since \(\sqrt{25}=c\) and \(\sqrt{25} = 5\).

Answer:

The first missing value (in \(16+\square = c^{2}\)) is \(9\), and the second missing value (in \(\square=c\)) is \(5\). So the completed steps are \(16 + 9=c^{2}\) and \(5=c\).