Answer:
(C) [tex]c(sin(B))=b(sin(C))[/tex]
Step-by-step explanation:
Given: In ΔABC, AD⊥BC.
To prove: [tex]\frac{sinB}{b}=\frac{sinC}{c}[/tex]
Proof:
Statement Reason
1. In ΔABC, AD⊥BC. Given
2. In ΔADB, [tex]sinB=\frac{h}{c}[/tex] Definition of sine
3. [tex]c(sinB)=h[/tex] Multiplicative property of equality
4. In ΔACD, [tex]sinC=\frac{h}{b}[/tex] Definition of sine
5. [tex]b(sinC)=h[/tex] Multiplicative property of equality
6. [tex]c(sin(B))=b(sin(C))[/tex] Substitution
7. [tex]\frac{sinB}{b}=\frac{sinC}{c}[/tex] Division property of equality.
Hence proved.
Therefore, option C is correct.
