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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
\(AB=34\)
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
\(AC=16\)

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