Question

find the value of tan c rounded to the nearest hundredth, if necessary. answer attempt 1 out of 3 tan c = submit answer

Explanation:

Step1: Find the length of AB

Use the Pythagorean theorem \(AB=\sqrt{AC^{2}-BC^{2}}\).
Given \(AC = 50\) and \(BC=14\), then \(AB=\sqrt{50^{2}-14^{2}}=\sqrt{(50 + 14)(50 - 14)}=\sqrt{64\times36}=\sqrt{2304}=48\).

Step2: Calculate \(\tan C\)

By the definition of the tangent function in a right - triangle \(\tan C=\frac{AB}{BC}\).
Since \(AB = 48\) and \(BC = 14\), then \(\tan C=\frac{48}{14}\approx3.43\).

Answer:

\(3.43\)