If t=38.5 and s=31.4 , find s. round to the nearest tenth.

a. 53.6'

b. 56.6'

c. 54.6'

d. 55.6'

show work!

choice C) 54.6 degrees

This value is approximate




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.