Question

turner is fishing from a small boat. a fish swimming at the same depth as the hook at the end of his fishing line is 5 meters away from the hook. if turner is 13 meters away from the fish, how far below turner is the hook? meters

Explanation:

Step1: Apply Pythagorean theorem

Let \(a = 5\) (distance between hook and fish), \(c=13\) (distance between Turner and fish). We need to find \(b\) (distance between Turner and hook). By Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), so \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(a = 5\) and \(c = 13\) into \(b^{2}=c^{2}-a^{2}\). Then \(b^{2}=13^{2}-5^{2}=169 - 25\).

Step3: Calculate \(b^{2}\) and \(b\)

\(b^{2}=144\), so \(b=\sqrt{144}\).

Answer:

\(12\)