Question

find the value of tan c rounded to the nearest hundredth, if necessary.

Explanation:

Step1: Find side AB using Pythagorean theorem

In right - triangle ABC, by 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

The tangent of an angle in a right - triangle is defined as the ratio of the opposite side to the adjacent side. For \(\angle C\), \(\tan C=\frac{AB}{BC}\). Since \(AB = 48\) and \(BC = 14\), then \(\tan C=\frac{48}{14}=\frac{24}{7}\approx3.43\).

Answer:

\(3.43\)