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PSYCHO15rus [73]
3 years ago
14

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

Mathematics
2 answers:
vitfil [10]3 years ago
5 0
Refer to the diagram below.

Let x = length of line segment RS.
Let Q = ∠RQS.
Let S = ∠RSQ

According to the Law of Sines,
\frac{sinS}{2.4} = \frac{sin80^{o}}{3.1} \\\\sinS = (\frac{2.4}{3.1}) sin 80^{o}= 0.7624 \\\\ S = sin^{-1}0.7624 = 49.68^{o}

Because the sum of angles in a triangle is 180°, therefore
∠Q = 180 -(80 + 49.68) = 50.32°

Apply the Law of Sines again to obtain
\frac{x}{sinQ} = \frac{3.1}{sin80^{o}} \\\\ x = ( \frac{sin50.32^{o}}{sin80^{o}})3.1 =  2.423

Answer: The length of RS = 2.4 (nearest tenth)

Ivahew [28]3 years ago
5 0

Answer:

Answer: The length of RS = 2.4 (nearest tenth)

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