What is the length of AC?

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.

We have that

sin ∠ABC=

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

sin ∠ABC=  equation 1

sin ∠ABC=  equation 2

equate equation 1 and equation 2



the answer is