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.
(1 point)
○ 216
○ 234
○ 14.7
○ 15.3

Explanation:

Step1: Recall Pythagorean Theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse, and \(a, b\) are the legs. Here, hypotenuse \(c = 15\), one leg \(a = 3\), find the other leg \(b\). Rearrange the formula: \(b=\sqrt{c^2 - a^2}\).

Step2: Substitute values

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

Step3: Calculate and round

\(\sqrt{216}\approx14.7\) (rounded to the nearest tenth).

Answer:

14.7