Question

the equation \\(\tan(55^{\circ}) = \frac{15}{b}\\) can be used to find the length of \\(\overline{ac}\\). what is the length of \\(\overline{ac}\\)? round to the nearest tenth. \\(\bigcirc\\) 3.0 cm. \\(\bigcirc\\) 9.8 cm. \\(\bigcirc\\) 10.5 cm. \\(\bigcirc\\) 12.8 cm.

Explanation:

Step1: Rearrange for $b$

Rearrange the tangent equation to isolate $b$.
$$b = \frac{15}{\tan(55^\circ)}$$

Step2: Calculate $\tan(55^\circ)$

Find the value of $\tan(55^\circ)$ (approx. 1.4281).
$$\tan(55^\circ) \approx 1.4281$$

Step3: Compute $b$

Divide 15 by the tangent value.
$$b \approx \frac{15}{1.4281} \approx 10.5$$

Answer:

10.5 cm.