ANSWER
Options 1 and 4
EXPLANATION
First, let us find the length of the third side of the right triangle. To do this apply the Pythagoras theorem.
Let the length of the third side of the triangle be x.
It implies that:
[tex]\begin{gathered} x^2+8^2=17^2 \\ x^2=17^2-8^2 \\ x^2=289-64=225 \\ x=\sqrt[]{225} \\ x=15 \end{gathered}[/tex]
Now, we can find the value of sinA, tanA, and sinC.
According to trigonometric ratios, SOHCAHTOA, we have that:
[tex]\begin{gathered} \sin A=\frac{\text{opposite}}{\text{hypotenuse}} \\ \tan A=\frac{\text{opposite}}{\text{adjacent}} \\ \sin C=\frac{\text{opposite}}{\text{hypotenuse}} \end{gathered}[/tex]
Therefore:
[tex]\begin{gathered} \sin A=\frac{15}{17} \\ \tan A=\frac{15}{8} \\ \sin C=\frac{8}{17} \end{gathered}[/tex]
Hence, the correct options are options 1 and 4.
