Question

use the image to answer the question. apply the pythagorean theorem to find the unknown side length in the given triangle. round your answer to the nearest tenth.

Explanation:

Step1: Recall the Pythagorean Theorem

The Pythagorean Theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (the side opposite the right - angle, \(c = 15\) here) and \(a\) and \(b\) are the legs of the right - triangle. Let \(a = 3\) and \(b\) be the unknown side. Then the formula becomes \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute the values into the formula

Substitute \(c = 15\) and \(a = 3\) into \(b=\sqrt{c^{2}-a^{2}}\). So \(b=\sqrt{15^{2}-3^{2}}=\sqrt{225 - 9}=\sqrt{216}\).

Step3: Calculate the square root

\(\sqrt{216}\approx14.7\) (using a calculator, \(\sqrt{216}=\sqrt{36\times6}=6\sqrt{6}\approx6\times2.45 = 14.7\)).

Answer:

\(14.7\)