Question 1202951
sin^(-1)(2/5) = 23.57017848 degrees.
sin^*(-1)(sqrt(21)/5) = 66.42182152 degrees.
23.57017848 degrees + 66.42182152 degrees = 90 degrees.
that's your solution.
the angles are complementary.
if you put them in the same right triangle, your triangle would have:
angle A = 23.57017847
angle B = 66.42182152
angle C = 90
given that sin(23.57017848) = 2/5, you have side opposite angle A = 2 and side opposite angle C = 5
given that sin(66.42182152) = sqrt(21) / 5, you have side opposite angle B = sqrt(21) and side opposite angle C = 5.
since side opposite angle A squared plus side opposite angle B squared = side opposite angle C squared, you get (2/5)^2 + (sqrt(21)/5)^2 = 5^2.
this becomes 4/25 + 21/25 = 25 which is true, confirming the value of the angles is correct.