Question

what is the length of \\(\overline{ac}\\)? round to the nearest tenth.\
\
\\(\bigcirc\\) 10.5 m\
\\(\bigcirc\\) 12.3 m\
\\(\bigcirc\\) 18.3 m\
\\(\bigcirc\\) 21.4 m

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \(ABC\) (right - angled at \(C\)), we know angle \(A = 55^{\circ}\), side \(BC=15\) m (opposite to angle \(A\)), and we want to find \(AC\) (adjacent to angle \(A\)). The trigonometric ratio that relates the opposite side and the adjacent side of an angle in a right triangle is the tangent function. The formula for tangent is \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan(55^{\circ})=\frac{BC}{AC}\).

Step2: Solve for \(AC\)

We know that \(BC = 15\) m and \(\theta=55^{\circ}\). From \(\tan(55^{\circ})=\frac{15}{AC}\), we can re - arrange the formula to solve for \(AC\). Cross - multiplying gives us \(AC=\frac{15}{\tan(55^{\circ})}\).
We know that \(\tan(55^{\circ})\approx1.4281\). Then \(AC = \frac{15}{1.4281}\approx10.5\) m.

Answer:

10.5 m