Answer: choice C) 54.6 degrees
This value is approximate
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Explanation:
Segment lower case 's' is opposite angle upper case "S"
So if angle S is the reference angle, then 's' is the opposite side
t is always the hypotenuse no matter what the reference angle is
we'll use the sine rule
sin(angle) = opposite/hypotenuse
sin(S) = s/t
sin(S) = 31.4/38.5
sin(S) = 0.81558441558441
Now apply the arcsine rule to both sides. Make sure your calculator is in degree mode
sin(S) = 0.81558441558441
arcsin(sin(S)) = arcsin(0.81558441558441)
S = 54.6451886235083
S = 54.6 ... round to the nearest tenth
So that's why angle S is roughly 54.6 degrees, which points to the answer being choice C.
