Question

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

Explanation:

Step1: Identify the hypotenuse and legs

The hypotenuse is the longest side of a right - triangle. Here, assume the hypotenuse $c = 18$ and one leg $a = 12$. We want to find the other leg $b$.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. Rearranging for $b$, we get $b=\sqrt{c^{2}-a^{2}}$.
Substitute $a = 12$ and $c = 18$ into the formula: $b=\sqrt{18^{2}-12^{2}}=\sqrt{(18 + 12)(18 - 12)}=\sqrt{30\times6}=\sqrt{180}$.

Step3: Calculate the value of $b$

$\sqrt{180}\approx13.4$

Answer:

$13.4$