Question

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

Explanation:

Step1: Use cosine formula

In a right - triangle \(ABC\) (\(\angle B = 90^{\circ}\)), \(\cos C=\frac{BC}{AC}\). Given \(BC = 44\), \(\angle C=46^{\circ}\), and \(AC=x\).
So, \(\cos46^{\circ}=\frac{44}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x=\frac{44}{\cos46^{\circ}}\).
We know that \(\cos46^{\circ}\approx0.6947\).
Then \(x=\frac{44}{0.6947}\approx63.3\).

Answer:

\(x\approx63.3\)