Question

In right ∆ABC, C is a right angle and sin A = 243/312 . What is m∠B

Answer 1

get value of 'A' from a sin table and C is already given 90, hence B can be calculated using angle sum property of a triangle. 
alternately, using pythagorus th., find the third side of triangle and then you will know sinB. 
again from sin table, get B

sinA = 243/312 = 0.7788 
A = 51.16 degrees 
B = 180 - 90 - 51.16 = 38.64 degrees (fourth choice) 

Answer 2

if sinA=243/312

A=arcsin(243/312)  and since B is complementary we can say:

B=90-A

B=90-arcsin(243/312)

B≈38.84°  (to nearest one-hundredth of a degree)