Question

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 1

Angle C is 101 degrees

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) =
`(BD)/(CD)`

Tan(BCD) =
`(11.86828)/(2.30506)`

Tan(BCD) =
`(11.86828)/(2.30506)`=5.1487

Angle BCD = 79.00

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

Angle C is 101 degrees