Respuesta :

mhanifa

Answer:

  • (A) 44.7°

Step-by-step explanation:

Use the law of cosines:

  • [tex]cos A=(b^2+c^2-a^2)/(2bc)[/tex]
  • [tex]cos A=(25^2+31^2-22^2)/(2*25*31)=0.711[/tex]
  • m∠A = arccos(0.711) ≈ 44.7°

Using law of cosines

[tex]\\ \sf\longmapsto cosA=\dfrac{b^2+c^2-a^2}{2bc}[/tex]

[tex]\\ \sf\longmapsto cosA=\dfrac{25^2+31^2-32^2}{2(25)(31)}[/tex]

[tex]\\ \sf\longmapsto cosA=\dfrac{625+961-484}{1550}[/tex]

[tex]\\ \sf\longmapsto cosA=\dfrac{1102}{1550}[/tex]

[tex]\\ \sf\longmapsto cosA=0.7109[/tex]

[tex]\\ \sf\longmapsto A=cos^{-1}(0.7109)[/tex]

[tex]\\ \sf\longmapsto A=44.7°[/tex]

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