What is the length of line segment rs? use the law of sines to find the answer. round to the nearest tenth.

Step-by-step explanation:

The law of sines is given by the formula;

where A,B,C are the interior angles of triangle ABC and are the sides opposite these angles.

Applying the sine rule to ΔQRS, we obtain;

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The sum of angles in a triangle is 180 degrees.

We use the sine rule again

To the nearest tenth

The length of segment RS is:

                              2.4 units.

Step-by-step explanation:

We will use the Law of Cosine to find the length of segment RS.

Let the  segment RS be denoted by 'c'.

Let a=RQ=2.4 units.

b=QS=3.1 units.

Now, according to the law of cosine we have:

On equating the first two equalities we have:

Hence, on solving we get:

S=49.68°

Now as we know that in a triangle the sum of all the angles of a triangle is:

180 degree.

Hence,

∠Q+∠R+∠S=180°

⇒   ∠Q+80°+49.68°=180°

⇒  ∠Q=50.32°

Similarly, on equating the second and third equality we have:

          Hence, the length of line segment is:

                             2.4 units.

step-by-stp

the correct answer is the section c