Question

what is the length of \\(\overline{ac}\\)? round to the nearest tenth.
triangle abc with right angle at c, angle at a is 55°, side bc is 15 m. four options: 10.5 m, 12.3 m, 18.3 m, 21.4 m

Explanation:

Step1: Identify the trigonometric ratio

We have a right triangle \( \triangle ABC \) with \( \angle C = 90^\circ \), \( \angle A = 55^\circ \), and \( BC = 15 \) m. We need to find \( AC \). Let's denote \( AC = x \). We know that \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). For \( \angle A \), the opposite side is \( BC \) and the adjacent side is \( AC \). So \( \tan(55^\circ)=\frac{BC}{AC} \)

Step2: Substitute the known values

We know \( BC = 15 \) m and \( \tan(55^\circ)\approx1.4281 \). So we have the equation \( 1.4281=\frac{15}{x} \)

Step3: Solve for \( x \)

Cross - multiply to get \( x\times1.4281 = 15 \). Then \( x=\frac{15}{1.4281}\approx10.5 \) (rounded to the nearest tenth)

Answer:

\( 10.5 \) m