Answer:
[tex]RS=2.4\ units[/tex]
Step-by-step explanation:
The complete question is
What is the length of line segment RS? Use the law of sines to find the answer. Round to the nearest tenth.
see the attached figure to better understand the problem
step 1
Find the measure of angle S
Applying the law of sines
[tex]\frac{QS}{sin(R)}=\frac{QR}{sin(S)}[/tex]
substitute the given values
[tex]\frac{3.1}{sin(80^o)}=\frac{2.4}{sin(S)}[/tex]
Solve for sin(S)
[tex]sin(S)=\frac{sin(80^o)}{3.1}(2.4)[/tex]
[tex]S=sin^{-1}[sin(80^o)}{3.1}(2.4)][/tex]
[tex]S=49.68^o[/tex]
step 2
Find the measure of angle Q
Remember that the sum of the interior angles in any triangle mut b equal to 180 degrees
so
[tex]m\angle Q+m\angle R+m\angle S=180^o[/tex]
substitute the given values
[tex]m\angle Q+80^o+49.68^o=180^o[/tex]
[tex]m\angle Q+129.68^o=180^o[/tex]
[tex]m\angle Q=180^o-129.68^o[/tex]
[tex]m\angle Q=50.32^o[/tex]
step 3
Find the length of segment RS
Applying the law of sines
[tex]\frac{QS}{sin(R)}=\frac{RS}{sin(Q)}[/tex]
substitute the given values
[tex]\frac{3.1}{sin(80^o)}=\frac{RS}{sin(50.32^o)}[/tex]
[tex]RS=\frac{3.1}{sin(80^o)}{sin(50.32^o)}[/tex]
[tex]RS=2.4\ units[/tex]
