Question

use the law of sines to solve the following problem. if $\angle c = 28$ degrees and side $c = 28$ m, then what is the length of side $a$ to the nearest meter? (1 point) \bigcirc 15 m \bigcirc 25 m \bigcirc 62 m \bigcirc 53 m

Explanation:

Step1: Identify triangle angles

First, correct the notation: the right angle is $\angle B = 90^\circ$, $\angle A = 28^\circ$, side $a$ is opposite $\angle A$, side $c=28\ \text{m}$ is adjacent to $\angle A$ (opposite $\angle C$ where $\angle C = 180^\circ - 90^\circ - 28^\circ = 62^\circ$).
Law of Sines: $\frac{a}{\sin A} = \frac{c}{\sin C}$

Step2: Rearrange to solve for $a$

Isolate $a$ using cross-multiplication.
$a = \frac{c \cdot \sin A}{\sin C}$

Step3: Substitute values and calculate

Plug in $c=28$, $\angle A=28^\circ$, $\angle C=62^\circ$.
$a = \frac{28 \cdot \sin(28^\circ)}{\sin(62^\circ)}$
$\sin(28^\circ) \approx 0.4695$, $\sin(62^\circ) \approx 0.8829$
$a \approx \frac{28 \cdot 0.4695}{0.8829} \approx \frac{13.146}{0.8829} \approx 14.89 \approx 15$

Answer:

15 m