Question

what is the length of $overline{ac}$? round to the nearest tenth. a 55° c 15 m b 10.5 m 12.3 m 18.3 m 21.4 m

Explanation:

Step1: Identify the trigonometric relation

In right - triangle \(ABC\) with right - angle at \(C\), we know \(\tan A=\frac{BC}{AC}\). Given \(\angle A = 55^{\circ}\) and \(BC = 15\) m. So, \(\tan55^{\circ}=\frac{15}{AC}\).

Step2: Solve for \(AC\)

We know that \(\tan55^{\circ}\approx1.4281\). Then, \(AC=\frac{15}{\tan55^{\circ}}\). Substituting the value of \(\tan55^{\circ}\), we get \(AC=\frac{15}{1.4281}\approx10.5\) m.

Answer:

10.5 m