Question

if the legs of a right triangle are both 1 unit long, what is the length of the hypotenuse? a. √2 b. √3 c. √4 d. √5 what is the pythagorean theorem used for? a. determining the hypotenuse in right triangles b. finding the area of a triangle c. calculating the circumference of a circle d. solving right triangles

Explanation:

Step1: Recall Pythagorean Theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\).

Step2: Substitute values

Given \(a = 1\) and \(b = 1\), then \(1^{2}+1^{2}=c^{2}\), so \(1 + 1=c^{2}\), \(c^{2}=2\), and \(c=\sqrt{2}\).

Step3: Recall Pythagorean Theorem usage

The Pythagorean Theorem \(a^{2}+b^{2}=c^{2}\) is mainly used to determine the length of the hypotenuse in right - triangles when the lengths of the two legs are known.

Answer:

1. A. \(\sqrt{2}\)
2. A. Determining the hypotenuse in right triangles