Respuesta :

lulu1991
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.
calculista
we have that
[tex]AB=34[/tex]
sin ∠ABC=[tex] \frac{8}{17} [/tex]

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

sin ∠ABC=[tex] \frac{8}{17} [/tex]  equation 1

sin ∠ABC=[tex] \frac{AC}{34} [/tex]  equation 2

equate equation 1 and equation 2

[tex] \frac{8}{17} = \frac{AC}{34} \\ \\ AC=34* \frac{8}{17} \\ \\ AC=16[/tex]

the answer is
[tex]AC=16[/tex]