Question

Find the exact value of sin A in simplest radical form.​

Answer 1

Using the law of sines, we have

$\dfrac{AB}{\sin(C)}=\dfrac{BC}{\sin(A)}$

And we know that

$AB=\sqrt{85},\quad BC=6,\quad A=90$

So, the equation becomes

$\sin(A)=\dfrac{BC\sin(C)}{AB}=\dfrac{6\sin(90)}{\sqrt{85}}=\dfrac{6}{\sqrt{85}}$