Question

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

Explanation:

Step1: Use trigonometric ratio (tangent)

In a right - triangle \(ABC\) with \(\angle B = 90^{\circ}\), \(\tan C=\frac{AB}{BC}\). Given \(BC = 44\), \(\angle C=46^{\circ}\), and \(AB = x\). The formula for tangent is \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan(46^{\circ})=\frac{x}{44}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\tan(46^{\circ})=\frac{x}{44}\) by \(44\). We get \(x = 44\times\tan(46^{\circ})\). Since \(\tan(46^{\circ})\approx1.0355\), then \(x=44\times1.0355\).

$$x = 45.562$$

Answer:

\(x\approx45.6\)