Question

what is the length of (overline{ac})? round to the nearest tenth.
image of a right triangle with vertices a, c, b (right angle at c), angle at a is (55^circ), side (bc = 15) m
options:

• (10.5) m
• (12.3) m
• (18.3) m
• (21.4) m

Explanation:

Step1: Identify triangle type and trigonometric ratio

This is a right - triangle \( \triangle ABC \) with \( \angle C = 90^{\circ} \), \( \angle A=55^{\circ} \), and \( BC = 15\space m \). We want to find \( AC \). We can use the tangent function, where \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}} \). For \( \angle A \), the opposite side is \( BC \) and the adjacent side is \( AC \). So \( \tan(55^{\circ})=\frac{BC}{AC} \).

Step2: Solve for \( AC \)

We know that \( BC = 15\space m \) and \( \tan(55^{\circ})\approx1.4281 \). From \( \tan(55^{\circ})=\frac{15}{AC} \), we can re - arrange the formula to solve for \( AC \): \( AC=\frac{15}{\tan(55^{\circ})} \).

Substitute \( \tan(55^{\circ})\approx1.4281 \) into the formula: \( AC=\frac{15}{1.4281}\approx10.5\space m \)

Answer:

10.5 m