Question

What is the length of AC?

Answer 1

The sin <ABC means that AC/AB. So we know AB=34. AC/AB=8/17. So the length of AC is 16. cos<ABC means BC/AB. tan<ABC means AC/BC.

Answer 2

We have that
$AB=34$
sin ∠ABC=$\frac{8}{17}$

we know that
in the right triangle ABC
sin ∠ABC is equal to  $\frac{AC}{AB}$
AC is the opposite side angle B
AB is the Hypotenuse

sin ∠ABC=$\frac{8}{17}$  equation 1

sin ∠ABC=$\frac{AC}{34}$  equation 2

equate equation 1 and equation 2

$\frac{8}{17} = \frac{AC}{34} \\ \\ AC=34* \frac{8}{17} \\ \\ AC=16$

the answer is
$AC=16$