In ⊙H, Arc I K ≅ Arc J K, mArc I K = (11x + 2)°, and mArc J K = (12x – 7)°.
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In all right triangles, the ratio between a leg and the hypothenuse is the sine of the angle opposite to the leg.
So, in your case, we have
In order to find XY, we have
So, the ratio for the sine is