Question

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'


Please show work!

Answer 1

Answer: choice C) 54.6 degrees

This value is approximate

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Step-by-step 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.