Question

value: 10
find the length of the segment indicated. round to the nearest tenth if necessary.

Explanation:

Step1: Apply the Pythagorean theorem

In a right - triangle formed within the circle, if the radius of the circle is \(r = 5\) and one of the legs of the right - triangle is \(a = 3\), and the other leg is \(x\). The Pythagorean theorem is \(a^{2}+x^{2}=r^{2}\).
So, \(x=\sqrt{r^{2}-a^{2}}\).

Step2: Substitute the values

Substitute \(r = 5\) and \(a = 3\) into the formula \(x=\sqrt{r^{2}-a^{2}}\).
We get \(x=\sqrt{5^{2}-3^{2}}=\sqrt{25 - 9}=\sqrt{16}\).

Step3: Calculate the value

\(\sqrt{16}=4\).

Answer:

4