Question

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

Explanation:

Step1: Identify trigonometric ratio

In right triangle \(ABC\), \(\tan(C)=\frac{AB}{BC}\). Here, \(AB = 12\), \(BC=x\), and \(\angle C = 61^\circ\). So \(\tan(61^\circ)=\frac{12}{x}\).

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:

\(6.7\)