In triangle abc , side BC is 3 inches long and side AB is 16 inches long. Angle A measures 20 °. Given that angle C is an obtuse angle, find the measure of angle C. Round to the nearest tenth of a degree

Answer:Angle C is 101 degrees Step-by-step explanation:Given triangle ABC,Side BC =3Side AB =16Angle A=20Also, Angle C is an obtuse angle.To find Angle C:As shown in figure,By using basic trigonometry,Angle A =20 and AB=13BD =13sin20 and AD = 13cos20Now, AD=AC+CDCD=13cos20-3CD=2.30506And BD =13sin20=11.86828In triangle BDC, Tan(BCD) = [tex]\frac{BD}{CD}[/tex]Tan(BCD) = [tex]\frac{11.86828}{2.30506}[/tex]Tan(BCD) = [tex]\frac{11.86828}{2.30506}[/tex]=5.1487Angle BCD = 79.00Therefore, Angle BCA =180-Angle BCD=180-79=101.Angle C is 101 degrees