Well, darling, the cosecant (csc) of a 63 degree angle is simply 1/sin(63). So, grab your calculator and divide 1 by the sine of 63 degrees to get your answer. Math doesn't have to be a drag, honey!
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You can calculate this on any scientific calculator. Those calculators don't usually have a special key for the cosecans, but this is the same as 1 / sin(63).
csc(74) = 1.0403 (rounded)
2.281
.835807361
A pair of supplementary angles add up to 180 degrees. Therefore, the supplement to a 63 degree angle is equal to 180 - 63 = 117 degrees.
It's an acute angled triangle...