Question

proof:

statements	reasons
2. $angle adc$ and $angle bdc$ are right angles.	definition of altitude
3. $\triangle adc$ and $\triangle bcd$ are right triangles.	definition of right triangles
4. $sin(a) = \frac{cd}{b}$, $sin(b) = \frac{cd}{a}$	definition of sine
5. $cd = b \sin(a)$, $cd = a \sin(b)$	multiplication property of equality
6.?	substitution property of equality
7. $\frac{a}{\sin(a)} = \frac{b}{\sin(b)}$	cross product property

which statement completes this proof?

a. $b \sin(a) = a \sin(b)$

b. $\frac{cd}{b} = \frac{cd}{a}$

c. $\frac{b}{cd} = \frac{a}{cd}$

d. $b \sin(b) = a \sin(a)$

Explanation:

Step1: Recall Step 5 results

From step 5, we have \( CD = b\sin(A) \) and \( CD = a\sin(B) \).

Step2: Apply Substitution Property

The substitution property of equality allows us to set the two expressions for \( CD \) equal to each other. So, substitute \( CD \) from both equations: \( b\sin(A)=a\sin(B) \).

Answer:

A. \( b \sin (A) = a \sin (B) \)