Question

1. solve for ( x ). round to the nearest tenth, if necessary.

Explanation:

Step1: Recall tangent definition

In a right triangle, \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle C = 61^\circ\), opposite side to \(\angle C\) is \(AB = 12\), adjacent side is \(BC=x\). So \(\tan(61^\circ)=\frac{AB}{BC}=\frac{12}{x}\).

Step2: Solve for x

Rearrange the formula: \(x=\frac{12}{\tan(61^\circ)}\). Calculate \(\tan(61^\circ)\approx1.8040\). Then \(x=\frac{12}{1.8040}\approx6.7\).

Answer:

\(x\approx6.7\)