Question

math notes
right triangle with leg a, leg b, hypotenuse c, 90° right angle, and formula ( a^2 + b^2 = c^2 )

Explanation:

Since the problem (or the image) seems to be about the Pythagorean theorem for a right - triangle, if we assume we need to identify the theorem or use it (but no specific calculation - based question is given yet). If we consider a common problem like finding the length of one side when the other two are known, for example, if \(A = 3\), \(B = 4\), let's show the step - by - step to find \(C\):

Step 1: Recall the Pythagorean theorem

The Pythagorean theorem for a right - triangle is given by \(A^{2}+B^{2}=C^{2}\). Given \(A = 3\) and \(B = 4\), we first calculate \(A^{2}\) and \(B^{2}\).
\(A^{2}=3^{2}=9\), \(B^{2}=4^{2} = 16\)

Step 2: Calculate the sum of \(A^{2}\) and \(B^{2}\)

We add the two values we just calculated: \(A^{2}+B^{2}=9 + 16=25\)

Step 3: Find the value of \(C\)

Since \(A^{2}+B^{2}=C^{2}\) and \(A^{2}+B^{2}=25\), then \(C^{2}=25\). Taking the square root of both sides (and since \(C\) represents the length of a side of a triangle, we take the positive square root), we get \(C=\sqrt{25} = 5\)

If the question was to identify the theorem, the answer would be the Pythagorean theorem which states that in a right - angled triangle, the square of the hypotenuse (the side opposite the right angle, \(C\)) is equal to the sum of the squares of the other two sides (\(A\) and \(B\)), i.e., \(A^{2}+B^{2}=C^{2}\).

Since the original problem was not fully specified (the image shows the Pythagorean theorem for a right - triangle), if we assume a common calculation - based problem:

Answer:

If \(A = 3\), \(B = 4\), then \(C = 5\) (using the Pythagorean theorem \(A^{2}+B^{2}=C^{2}\))