Question

find the length of the third side. if necessary, round to the nearest tenth.
2
4

Explanation:

Step1: Identify triangle type (right triangle)

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with legs of lengths \(a\) and \(b\) and hypotenuse of length \(c\), \(a^{2}+b^{2}=c^{2}\). Here, the hypotenuse \(c = 4\) and one leg \(a=2\), and we need to find the other leg \(b\).
Rearranging the Pythagorean theorem to solve for \(b\), we get \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute the values

Substitute \(c = 4\) and \(a = 2\) into the formula:
\(b=\sqrt{4^{2}-2^{2}}=\sqrt{16 - 4}=\sqrt{12}\)

Step3: Simplify and round

Simplify \(\sqrt{12}\approx3.5\) (rounded to the nearest tenth)

Answer:

The length of the third side is approximately \(3.5\)