We know that the given triangles are similar. That means Angles Y and B are congruent. So, our job is to find Angle B first using trigonometric reasons. Let's use the tangent which is equal to the ratio between the opposite leg and the adjacent leg to angle B
[tex]\begin{gathered} \text{tan(B)=}\frac{14.7}{14}=1.05=\tan Y \\ B=\tan ^{-1}(1.05)\approx46.4 \end{gathered}[/tex]
Which means angle Y is also 46.4°, approximately. Also, the tangent of Y is 1.05 too, because Y and B are congruent. Now, let's find the sine and cosine of B or Y (remember they are equal).
[tex]\sin B=\frac{14.7}{20.3}\approx0.72=\sin Y[/tex][tex]\cos B=\frac{14}{20.3}\approx0.69=\cos Y[/tex]
Therefore, the tanY is 1.05, sinY is 0.72 and cosY 0.69.
