>>16996203 1. Get a protractor that is divided to show 28 degree 2. draw that unit circle. 3. measure that vertical length labeled sin with a metered ruler divided by the unit circles radius? Before calculator they either use some good enough approximation or look up in pronted look up table
>>16996203 As others mentioned, lookup tables existed. Hell, any textbook that addresses trig functions more than likely has a lookup table somewhere in the index.
Other than that, the test makers would be aware what the students had available to them. They wouldn't ask a question which requires a calculator in a time when calculators didn't exist. If contemporary tools made the problem tedious and take a long time, there'd be fewer questions like that.