Question

find the length of the third side. if necessary, round to the nearest tenth.

Explanation:

Step1: Identify triangle type

It's a right - triangle, so use Pythagorean theorem: \(a^{2}+b^{2}=c^{2}\), where \(c\) is hypotenuse, \(a,b\) are legs. Here, \(c = 21\), \(a = 17\), find \(b\).

Step2: Rearrange formula

\(b=\sqrt{c^{2}-a^{2}}\)

Step3: Substitute values

\(c = 21\), \(a = 17\), so \(b=\sqrt{21^{2}-17^{2}}=\sqrt{(21 + 17)(21 - 17)}=\sqrt{38\times4}=\sqrt{152}\)

Step4: Calculate and round

\(\sqrt{152}\approx12.3\)

Answer:

The length of the third side is approximately \(12.3\)