Question

what is the length of ac? round to the nearest tenth. 10.5 m 12.3 m 18.3 m 21.4 m

Explanation:

Step1: Use tangent function

In right - triangle \(ABC\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 55^{\circ}\), the adjacent side to \(\angle B\) is \(AC\) and the opposite side is \(BC = 15\)m. So, \(\tan(55^{\circ})=\frac{BC}{AC}\).

Step2: Rearrange for \(AC\)

We know that \(AC=\frac{BC}{\tan(55^{\circ})}\). Since \(\tan(55^{\circ})\approx1.4281\) and \(BC = 15\)m, then \(AC=\frac{15}{\tan(55^{\circ})}\approx\frac{15}{1.4281}\approx10.5\)m.

Answer:

\(10.5\)m