Question

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

a 55° c
15 m
b
10.5 m
12.3 m
18.3 m
21.4 m

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle, with $\angle A = 55^\circ$, opposite side $BC = 15$ m, and $AC$ is the adjacent side. Use tangent:
$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Step2: Rearrange to solve for $AC$

Isolate $AC$ from the tangent formula:
$AC = \frac{BC}{\tan(\angle A)}$

Step3: Substitute values and calculate

Plug in $BC=15$ and $\angle A=55^\circ$:
$AC = \frac{15}{\tan(55^\circ)}$
$\tan(55^\circ) \approx 1.4281$, so $AC \approx \frac{15}{1.4281} \approx 10.5$

Answer:

10.5 m