Question

solve for segment db

Explanation:

Step1: Identify triangle CBD

In right triangle \(CBD\), we know \(BC = 5\) and \(CD = 3\). We can use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a,b\) are the legs. Here, \(BC\) is the hypotenuse, \(CD\) and \(DB\) are the legs. So the formula for \(DB\) is \(DB=\sqrt{BC^{2}-CD^{2}}\).

Step2: Substitute values

Substitute \(BC = 5\) and \(CD = 3\) into the formula: \(DB=\sqrt{5^{2}-3^{2}}=\sqrt{25 - 9}=\sqrt{16}\).

Step3: Simplify the square root

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

Answer:

\(4\)