Question

use the pythagorean theorem to find the length of the hypotenuse of the triangle below.
(there is a right triangle with one leg 6 and the other leg 8, and a right angle symbol at the intersection of the two legs)
show your work here
hint: to add the square root symbol (√□), type root

Explanation:

Step1: Recall Pythagorean theorem

The Pythagorean theorem states that for a right - triangle with legs of length \(a\) and \(b\) and hypotenuse of length \(c\), \(c^{2}=a^{2}+b^{2}\). In this triangle, \(a = 6\) and \(b=8\).

Step2: Substitute values into the formula

Substitute \(a = 6\) and \(b = 8\) into the formula \(c^{2}=a^{2}+b^{2}\). We get \(c^{2}=6^{2}+8^{2}\). Calculate \(6^{2}=36\) and \(8^{2}=64\). Then \(c^{2}=36 + 64=100\).

Step3: Solve for c

Take the square root of both sides to find \(c\). Since \(c^{2}=100\), then \(c=\sqrt{100}=10\).

Answer:

The length of the hypotenuse is \(10\).