Question

solve for x. round to the nearest tenth, if necessary. a 12 b x c 61°

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, \(\tan C=\frac{AB}{BC}\). Here, \(AB = 12\), \(BC=x\), and \(C = 61^{\circ}\). So, \(\tan61^{\circ}=\frac{12}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x=\frac{12}{\tan61^{\circ}}\).
We know that \(\tan61^{\circ}\approx1.804\). Then \(x=\frac{12}{1.804}\approx6.7\).

Answer:

\(x\approx6.7\)