How did my teacher got that if sin α=0.4, α=23.58 degrees? All I am getting is sin(0.4)=0.006981260298
The way you are doing it 0.4 is the number of degrees and 0.0069etc is the sin of 0.4 degrees.
That is NOT the question
sin (alpha )= 0.4
0.4 is the sine of the angle - not the angle itself.
You need the Inverse sin of 0.4 to get the angle. Written sin -10.4
[do not confuse this with a power of -1]
This can also be called arc sin 0.4 or asin0.4
Anyway on your calculator press
shift sin 0.4 = and you will have your teacher's correct answer
If you then press the degress minutes and second button it will convert it for you int degrees minutes and seconds.
+118653 
