Solve for lenght y. show work

You have a right triangle here so we are going to use a trig identity to solve for y. Y is the side opposite the angle given to us, and then we also have the hypotenuse. Opposite / hypotenuse tells us that we have to use the sin ratio to find y. .

In order to isolate the y, we will multiply both sides by 37 to get

37sin(52)=y. We can do this on our calculator in degree mode and will get that y = 29.156 inches