What is the length of line segment RS? Use the law of sines to find the answer. Round to the nearest tenth.

Answer:
Step-by-step explanation:
The law of sines is given by the formula;[tex]\frac{a}{\sin(A)}=\frac{b}{\sin(B)}=\frac{c}{\sin(C)}[/tex]where A,B,C are the interior angles of triangle ABC and [tex]a,b,c[/tex] are the sides opposite these angles.
Applying the sine rule to ΔQRS, we obtain;[tex]\frac{2.4}{\sin(S)} =\frac{3.1}{\sin(80\degree)}[/tex].
[tex]2.4\times \sin(80\degree) =3.1\sin(S)[/tex].
[tex]2.3635=3.1\sin(S)[/tex].
[tex]\Rightarrow \frac{2.3635}{3.1}=\sin(S)[/tex].
[tex]0.7624=\sin(S)[/tex].

[tex]\Rightarrow \sin^{-1}(0.7624)=S[/tex].
[tex]\Rightarrow 49.676=S[/tex].
The sum of angles in a triangle is 180 degrees.[tex]<\:Q+49.676+80=180[/tex]
[tex]<\:Q=180-129.676[/tex]
[tex]\Rightarrow <\:Q=50.324[/tex]

We use the sine rule again
[tex]\frac{|RS|}{\sin(50.324\degree)}=\frac{3.1}{\sin(80\degree)}[/tex]
[tex]|RS|=\frac{3.1}{\sin(80\degree)}\times \sin(80\degree)[/tex]
[tex]|RS|=2.423[/tex]
To the nearest tenth
[tex]|RS|=2.4\:units[/tex]