Question

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

Explanation:

Step1: Use trigonometric ratio

In right - triangle \(ABC\) with \(\angle C = 46^{\circ}\), \(\text{adjacent side}=44\) and \(\text{opposite side}=x\). We use the tangent ratio \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). 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 \(x=44\times1.0355 = 45.562\approx45.6\).

Answer:

\(45.6\)