Question

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

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 \(c\), \(c^{2}=a^{2}+b^{2}\), and if we want to find the length of a leg, we can rearrange it as \(b = \sqrt{c^{2}-a^{2}}\) (assuming \(c\) is the hypotenuse and \(a\) is one of the legs). In the given triangle, the hypotenuse \(c = 4\) and one leg \(a=2\), and we need to find the other leg \(b\).

Step2: Apply Pythagorean theorem

Using the formula \(b=\sqrt{c^{2}-a^{2}}\), substitute \(c = 4\) and \(a = 2\) into the formula.

$$
LATEXBLOCK0
$$

Answer:

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