Question

Triangle A B C is shown. Angle A B C is 95 degrees and angle B C A is 45 degrees. The length of A B is c and the length of B C is 3.0 centimeters. Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction Which represents the value of c? C = StartFraction (3) sine (40 degrees) Over sine (45 degrees) EndFraction c = StartFraction (3) sine (45 degrees) Over sine (40 degrees) EndFraction c = StartFraction sine (40 degrees) Over (3) sine (45 degrees) EndFraction c = StartFraction sine (45 degrees) Over (3) sine (40 degrees)

Answer 1

B

Explanation:

Answer 2

(B)c = StartFraction (3) sine (45 degrees) Over sine (40 degrees) EndFraction

`c=(3 * \sin 45)/(sin 40)`

Explanation:

In Triangle ABC is shown.

`\angle A B C=` 95 degrees

`\angle B C A =` 45 degrees.

|AB|=c

|BC|=3.0 cm

`\angle A+\angle B+\angle C=180^\circ\\\angle A+95+45=180\\\angle A=180-140=40^\circ`

Using the Law of Sines

`(a)/(\sin A)=(b)/(\sin B)=(c)/(\sin C)`

`(3)/(\sin 40)=(c)/(\sin 45)\\\\$Cross multiply\\c*\sin 40 =3 * \sin 45\\\\c=(3 * \sin 45)/(sin 40)`

The correct option is B.