lovelylittleme
lovelylittleme lovelylittleme
  • 20-06-2022
  • Mathematics
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what is the length of the side labeled x cm ? show your work

what is the length of the side labeled x cm show your work class=

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monospace
monospace monospace
  • 20-06-2022

Answer:

9.9 cm

Step-by-step explanation:

Calculate the third angle and then use The Law of Sines.

Sum of angles in triangle is 180°.

angle + 40° + 63° = 180°

angle = 180° - 40° - 63°

angle = 77°

Now we can use the law of sines.

[tex]\frac{x}{\sin 40} = \frac{15}{\sin 77}[/tex]

[tex]x = \frac{15 \cdot \sin 40}{\sin 77}[/tex]

[tex]x \approx 9.895[/tex]

[tex]x \approx 9.9 \text{ cm}[/tex]

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