Question

what is the length of $overline{ac}$? round to the nearest tenth.

10.5 m
12.3 m
18.3 m
21.4 m

Explanation:

Step1: Identify the trigonometric relationship

In right - triangle ABC, we know the angle A = 55° and the side BC = 15 m. We want to find the side AC. Since $\tan A=\frac{BC}{AC}$, we can re - arrange the formula to solve for AC.

Step2: Apply the tangent formula

We know that $\tan A=\frac{BC}{AC}$, so $AC = \frac{BC}{\tan A}$. Substituting A = 55° and BC = 15 m, and $\tan55^{\circ}\approx1.4281$. Then $AC=\frac{15}{\tan55^{\circ}}=\frac{15}{1.4281}\approx10.5$ m.

Answer:

10.5 m