Solve for c.
Pythagorean Theorem: $a^2 + b^2 = c^2$
Round your answer to the nearest hundredth.
$c = [?]$
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse \(c\) is equal to the sum of the squares of the other two sides \(a\) and \(b\):
\[a^2 + b^2 = c^2\]
To find \(c\), we take the square root of both sides:
\[c = \sqrt{a^2 + b^2}\]
Since the specific values for \(a\) and \(b\) were not provided in the problem statement, I will demonstrate the solution using variables. If you have specific values, you can substitute them into this formula. For instance, if \(a = 3\) and \(b = 4\), the calculation would be:
\[c = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5.00\]
Rounding to the nearest hundredth, the final answer would be 5.00. Given the general nature of the request, the result remains the expression of the Pythagorean theorem.
The Pythagorean theorem is essential in many real-world applications, such as construction and navigation. For example, if you are building a ladder and need to know how long it should be to reach a window 4 meters high while being placed 3 meters away from the wall, you can use the theorem to find the length of the ladder: \(c = \sqrt{3^2 + 4^2} = 5\) meters. It's a fundamental tool for solving spatial problems!