Answer:
Using the Sine Rule , which states that
[tex]\frac{a}{Sin A}=\frac{b}{Sin B}=\frac{c}{SinC}[/tex]
In Δ ABC
∠A +∠B+∠C=180°→→Angle Sum Property of Triangle
72°+85°+∠C=180°
∠C=180° - 157°
∠C= 23°
All the angles are in degrees.
[tex]\frac{a}{Sin 72}=\frac{b}{Sin 85}=\frac{6.2}{Sin 23}[/tex]
Using the table of Sine, Calculating Sine Values
Sin 72°= 0.9510
Sin 85°=0.996
Sin 23°=0.390
[tex]\frac{a}{0.951}=\frac{b}{0.996}=\frac{6.2}{0.390}\\\\ a=\frac{6.2 * 0.951}{0.390}= 15.118\\\\ b=\frac{6.2 * 0.996}{0.390}=15.833[/tex]
Among the five Options,
Option E: a= 15.09 and b=15.81 is approximately true.
