Question

In triangle ABC below, sinC=h/a and sinA=h/c. Which of the following combines the two sine ratios into one equation?

Answer 1

We know:

$sin(C)=\frac{h}{a}$

and

$sin(A)=\frac{h}{c}$

These expressions have an $h$ term in common. We can combine them if we can find forms of the expressions in terms of $h$:

$h=a(sin(C))$

$h=c(sin(A))$

Now, because $h=h$ (by the reflexive property), we can write:

$a(sin(C))=c(sin(A))$

This is our answer, A.