Respuesta :
Answer:
(B)c = StartFraction (3) sine (45 degrees) Over sine (40 degrees) EndFraction
[tex]c=\dfrac{3 * \sin 45}{sin 40}[/tex]
Step-by-step explanation:
In Triangle ABC is shown.
[tex]\angle A B C=[/tex] 95 degrees
[tex]\angle B C A =[/tex] 45 degrees.
|AB|=c
|BC|=3.0 cm
[tex]\angle A+\angle B+\angle C=180^\circ\\\angle A+95+45=180\\\angle A=180-140=40^\circ[/tex]
Using the Law of Sines
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
[tex]\dfrac{3}{\sin 40}=\dfrac{c}{\sin 45}\\\\$Cross multiply\\c*\sin 40 =3 * \sin 45\\\\c=\dfrac{3 * \sin 45}{sin 40}[/tex]
The correct option is B.
