Question

Help!!! Trigonometry

Answer 1

3.

$sin\ A = \dfrac{opposite \angle A}{hypotenuse}=\dfrac{k}{c}\\\\\\sin\ C = \dfrac{opposite \angle C}{hypotenuse}=\dfrac{k}{a}$

4.

$sin\ A=\dfrac{k}{c}\quad \rightarrow \quad c\ sin\ A=k\\\\\\sin\ C=\dfrac{k}{a}\quad \rightarrow \quad a\ sin\ C=k$

5.

$c\ sin\ A=a\ sin\ C\\\\\dfrac{c\ sin\ A}{ac}=\dfrac{a\ sin\ C}{ac}\\\\\\\dfrac{sin\ A}{a}=\dfrac{sin\ C}{c}\quad \rightarrow \quad \text{NOTE: This is the Law of Sines}$