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

Answer:

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

$c=\dfrac{3 * \sin 45}{sin 40}$

Step-by-step 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

$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$

$\dfrac{3}{\sin 40}=\dfrac{c}{\sin 45}\\\\ Cross multiply\\c*\sin 40 =3 * \sin 45\\\\c=\dfrac{3 * \sin 45}{sin 40}$

The correct option is B.

Answer 2

Answer:

B

Step-by-step explanation: