Question

find the length of the third side. if necessary, write in simplest radical form. triangle image with two legs of length 1 and a right angle

Explanation:

Step1: Identify the triangle type

The triangle is a right triangle with two legs of length 1.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right triangle with legs \(a\) and \(b\), and hypotenuse \(c\), \(c = \sqrt{a^2 + b^2}\). Here, \(a = 1\) and \(b = 1\), so \(c=\sqrt{1^2 + 1^2}=\sqrt{1 + 1}=\sqrt{2}\).

Answer:

\(\sqrt{2}\)