Question

three ballet dancers are positioned on stage. austen is straight behind erica and directly left of kelly. if erica and austen are 9 meters apart, and kelly and erica are 15 meters apart, what is the distance between austen and kelly? meters

Explanation:

Step1: Identify the triangle type

The positions form a right triangle, with Erica - Austen as one leg (\(a = 9\) m), Erica - Kelly as the hypotenuse (\(c = 15\) m), and Austen - Kelly as the other leg (\(b\)).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is \(a^2 + b^2 = c^2\). Rearranging for \(b\), we get \(b = \sqrt{c^2 - a^2}\).

Step3: Substitute values

Substitute \(a = 9\) and \(c = 15\) into the formula:
\(b = \sqrt{15^2 - 9^2} = \sqrt{225 - 81} = \sqrt{144} = 12\).

Answer:

12