Question

the equation \\(\sin(25^{\circ}) = \frac{9}{c}\\) can be used to find the length of \\(\overline{ab}\\).
what is the length of \\(\overline{ab}\\)? round to the nearest tenth.
\\(\bigcirc\\) 19.3 in.
\\(\bigcirc\\) 21.3 in.
\\(\bigcirc\\) 23.5 in.
\\(\bigcirc\\) 68.0 in.

Explanation:

Step1: Rearrange for $c$

Rearrange the sine equation to solve for $c$ (which is $\overline{AB}$).
$$c = \frac{9}{\sin(25^\circ)}$$

Step2: Calculate $\sin(25^\circ)$

Find the decimal value of $\sin(25^\circ)$.
$\sin(25^\circ) \approx 0.4226$

Step3: Compute $c$

Divide 9 by the sine value.
$$c \approx \frac{9}{0.4226} \approx 21.3$$

Answer:

21.3 in.