Answer:
see below
Step-by-step explanation:
21) The law of sines can be used, since you have a side and its opposite angle.
sin(F)/DE = sin(D)/EF
F = arcsin(DE/EF·sin(D)) = arcsin(20/31·sin(95°)) ≈ 39.994°
E = 180° -95° -39.994° ≈ 45.006°
DF = sin(45.006°)/sin(95°)·31 ≈ 22.006
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22) The remaining two problems can be solved using the law of cosines:
c^2 = a^2 + b^2 - 2ab·cos(C)
Of course, c is the square root of the expression on the right.
EF = √(19^2 +35^2 -2(19)(35)cos(61°)) ≈ √(941.203) ≈ 30.679
Then an angle can be found using the law of sines
E ≈ arcsin(35/30.679·sin(61°)) ≈ 86.203°
F ≈ 180° -61° -86.203° ≈ 32.797°
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23) As in 22 …
RS = √(20^2 +28^2 -2(20)(28)cos(91°)) ≈ √(1203.547) ≈ 34.692
R ≈ arcsin(20/34.692·sin(91°)) ≈ 35.199°
S ≈ 180° -91° -35.199° ≈ 53.801°
