Question

find the value of tan c rounded to the nearest hundredth, if necessary. answer attempt 1 out of 2 tan c =

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 \(\tan C=\frac{opposite}{adjacent}\). For \(\angle C\), the opposite side is \(AB\) and the adjacent side is \(BC\). So \(\tan C=\frac{AB}{BC}\). Substituting \(AB = 48\) and \(BC = 14\), we get \(\tan C=\frac{48}{14}=\frac{24}{7}\approx3.43\).

Answer:

\(3.43\)