Question

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

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with hypotenuse \(c\) and legs \(a\) and \(b\), \(a^{2}+b^{2}=c^{2}\). Here, the hypotenuse \(c = 30\) and one leg \(b=18\), and we want to find the other leg \(a\).

Step2: Rearrange the Pythagorean theorem

We can rearrange the formula to solve for \(a\): \(a=\sqrt{c^{2}-b^{2}}\)

Step3: Substitute the values

Substitute \(c = 30\) and \(b = 18\) into the formula: \(a=\sqrt{30^{2}-18^{2}}=\sqrt{900 - 324}=\sqrt{576}\)

Step4: Calculate the square root

\(\sqrt{576}=24\)

Answer:

24