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

Question

contestada

Respuesta :

mintuchoubay mintuchoubay · Answer 1 · 2019-12-15T05:58:46+01:00

Answer:

Angle C is 101 degrees

Step-by-step explanation:

Given triangle ABC,

Side BC =3

Side AB =16

Angle A=20

Also, Angle C is an obtuse angle.

To find Angle C:

As shown in figure,

By using basic trigonometry,

Angle A =20 and AB=13

BD =13sin20 and AD = 13cos20

Now, AD=AC+CD

CD=13cos20-3

CD=2.30506

And BD =13sin20=11.86828

In 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]=5.1487

Angle BCD = 79.00

Therefore, Angle BCA =180-Angle BCD=180-79=101.

Angle C is 101 degrees