Question

7.1.ps-11 use the pythagorean theorem to find the unknown side of the right triangle. hypotenuse length = \boxed{} (simplify your answer. type exact answers, using radicals as needed.)

Explanation:

Step1: Recall Pythagorean Theorem

The Pythagorean Theorem states that for a right triangle with legs \(a\) and \(b\), and hypotenuse \(c\), \(a^2 + b^2 = c^2\). Here, \(a = 7\) and \(b = 24\).
\[
7^2 + 24^2 = c^2
\]

Step2: Calculate the squares

Calculate \(7^2 = 49\) and \(24^2 = 576\). Then add them together:
\[
49 + 576 = c^2
\]
\[
625 = c^2
\]

Step3: Solve for \(c\)

Take the square root of both sides. Since \(c\) is a length, we take the positive square root:
\[
c = \sqrt{625} = 25
\]

Answer:

25