Answered

IDNLearn.com is your reliable source for expert answers and community insights. Discover prompt and accurate answers from our experts, ensuring you get the information you need quickly.

Ivan began to prove the law of sines using the diagram and equations below.

[tex]\[
\begin{array}{l}
\sin (A) = \frac{h}{b} \quad \Rightarrow \quad b \sin (A) = h \\
\sin (B) = \frac{h}{a} \quad \Rightarrow \quad a \sin (B) = h
\end{array}
\][/tex]

Therefore, [tex]\(b \sin (A) = a \sin (B)\)[/tex].

Which equation is equivalent to [tex]\(b \sin (A) = a \sin (B)\)[/tex]?

A. [tex]\(\frac{a}{\sin (B)} = \frac{b}{\sin (A)}\)[/tex]

B. [tex]\(\frac{\sin (A)}{a} = \frac{\sin (B)}{b}\)[/tex]

C. [tex]\(\frac{\sin (A)}{\sin (B)} = \frac{b}{a}\)[/tex]

D. [tex]\(\frac{\sin (B)}{a} = \frac{\sin (A)}{b}\)[/tex]

Sagot :

GinnyAnsweridn
To determine an equivalent equation to [tex]\( b \sin(A) = a \sin(B) \)[/tex], let's go through a detailed, step-by-step reasoning process:

1. Starting Equation:
[tex]\[ b \sin(A) = a \sin(B) \][/tex]

2. To manipulate this equation into a different form, let's divide both sides by [tex]\(\sin(A) \sin(B)\)[/tex]:
[tex]\[ \frac{b \sin(A)}{\sin(A) \sin(B)} = \frac{a \sin(B)}{\sin(A) \sin(B)} \][/tex]

3. Simplifying both sides:
[tex]\[ \frac{b}{\sin(B)} = \frac{a}{\sin(A)} \][/tex]

This is the resulting equation that is equivalent to the original equation [tex]\( b \sin(A) = a \sin(B) \)[/tex].

Thus, the correct answer is:
[tex]\[ \frac{a}{\sin(B)} = \frac{b}{\sin(A)} \][/tex]

By following this reasoning step-by-step, we confirm that the equivalent equation is indeed:
[tex]\[ \frac{a}{\sin(B)} = \frac{b}{\sin(A)} \][/tex]
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your search for solutions ends here at IDNLearn.com. Thank you for visiting, and come back soon for more helpful information.