b=4.2cmc=3.5cmC=51°48′=51.8°
To solve for angle B, we use the sine rule,
sinBbsinB4.2sinBsinBB=sinCc=sin51.83.5=3.54.2×sin51.8=0.9430=70.6°
To solve for angle A,
Sum of internal angles in a triangle = 180°
∴ A + B + C = 180°
A = 180° - B - C
A = 180° - 70.6° - 51.8°
∴ A = 57.6°
To solve for side a, we use the sine rule;
sinAasin57.6aaa=sinCc=sin51.83.5=sin51.83.5×sin57.6=3.76cm
∴ a = 3.76cm, b = 4.2cm, c = 3.5cm
A = 57.6°, B = 70.6°, C= 51.8°
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