Question

a d c b bret kamala sin(c) = \frac{c}{h} sin(a) = \frac{a}{h} h = \frac{a}{sin(a)} h = \frac{c}{sin(c)} \frac{a}{sin(a)} = \frac{c}{sin(c)} \frac{sin(c)}{c} = \frac{sin(a)}{a} sin(c) = \frac{h}{a} sin(a) = \frac{h}{c} a sin(c) = h c sin(a) = h a sin(c) = c sin(a) \frac{sin(c)}{c} = \frac{sin(a)}{a} the proof was correctly completed by both bret and kamala the next step in the proof is to use the pythagorean theorem write an expression for the cosine of a draw in a new perpendicular line and write an expression for next

Explanation:

Step1: Analyze the sine - rule proof status

Both Bret and Kamala have correctly derived the sine - rule $\frac{\sin(C)}{c}=\frac{\sin(A)}{a}$. To further the proof in a triangle - related context, we consider the relationships between trigonometric functions.

Step2: Recall trigonometric identities

In a triangle, if we want to expand on the trigonometric relationships after establishing the sine - rule, writing an expression for the cosine of an angle is a logical next step as it helps in fully defining the triangle's trigonometric properties. Using the Pythagorean theorem is not directly related to the next step after the sine - rule proof, and drawing a new perpendicular line is not necessary at this stage.

Answer:

write an expression for the cosine of A