Question

use the pythagorean theorem to find the missing leg of the triangle below.
(image of a right triangle with one leg labeled 8, hypotenuse labeled 10, and the right angle at the bottom left corner)
show your work here
hint: to add the square root symbol (√□), type
oot\

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle with legs \(a\), \(b\) and hypotenuse \(c\), the theorem is \(a^{2}+b^{2}=c^{2}\). Let the missing leg be \(x\), one leg \(a = 8\), hypotenuse \(c=10\). So we have \(8^{2}+x^{2}=10^{2}\).

Step2: Solve for \(x^{2}\)

Calculate \(8^{2}=64\) and \(10^{2} = 100\). Then \(x^{2}=100 - 64\). So \(x^{2}=36\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{36}=6\).

Answer:

6