Writing trigonometric ratios - consider △xyz what are the ratios of sine, cosine, and tangent for angle y?

Hello!

Let's review our trigonometric ratios.

Let's look which lines are opposite, adjacent, and hypotenuse.

Opposite: XZ

Adjacent: YZ

Hypotenuse: XY

Let's plug these into our ratios.

As you can see, these numbers match answer C.

I hope this helps!

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47