Question

find the length of the unknown side. round your answer to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(c = 25\) cm and \(a=15\) cm, and we need to find \(b\). So, \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(c = 25\) and \(a = 15\) into the formula: \(b=\sqrt{25^{2}-15^{2}}=\sqrt{(25 + 15)(25 - 15)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)). Then \(b=\sqrt{40\times10}=\sqrt{400}=20\) cm.

Answer:

\(20\) cm