If angles C and D are the acute angles of a right triangle, we have the image as shown below:
The question gives that:
[tex]\sin D=\frac{2}{7}[/tex]
Comparing with the Sine Trigonometric Ratio given to be:
[tex]\sin \theta=\frac{opp}{hyp}[/tex]
we thus have that the Sine ratio of angle D in the triangle drawn above will be:
[tex]\sin D=\frac{d}{b}[/tex]
Hence, we can have the triangle look as shown below:
Therefore, the cosine of angle C, with the ratio:
[tex]\cos C=\frac{adj}{hyp}[/tex]
will be given to be:
[tex]\cos C=\frac{2}{7}[/tex]
Therefore, the correct option is the FIRST OPTION.
