ANSWER and EXPLANATION
We have the triangle given and we have to first label it for the missing angle.
The missing angle is 33 degrees and that is the measure of MNP.
Let us add it to the diagram:
Now, to find the correct ratio for each trigonometric value written, we apply trigonometric ratios SOHCAHTOA:
[tex]\begin{gathered} \sin (\theta)\text{ = }\frac{opposite}{hypotenuse} \\ \cos (\theta)\text{ = }\frac{adjacent}{hypotenuse} \\ \text{where }\theta\text{ = angle considered} \end{gathered}[/tex]
Therefore, we have that:
[tex]\begin{gathered} \sin 57\text{ = }\frac{15}{x} \\ \sin 33\text{ = }\frac{7}{x} \\ \cos 57\text{ = }\frac{7}{x} \\ \cos 33\text{ = }\frac{15}{x} \end{gathered}[/tex]
That is the correct ratio for each trigonometric value.
