Respuesta :

mhanifa

Answer:

  • 64.86°

Step-by-step explanation:

Use the law of cosines:

  • cos ∠B = (a² + c² - b²) / (2ac)
  • cos ∠B = (16² + 22² - 21²) / (2*16*22)
  • cos ∠B = 0.4247
  • m∠B = arccos 0.4247
  • m∠B = 64.86° (rounded to the nearest hundredths)

Here

  • a=22
  • b=21
  • c=16

Apply law of cosines

[tex]\ \ \sf\longmapsto cosB=\dfrac{a^2+b^2+c^2}{2ac}[/tex]

[tex]\ \ \sf\longmapsto cosB=\dfrac{22^2+21^2+16^2}{2(22)(16)}[/tex]

[tex]\ \ \sf\longmapsto cosB=\dfrac{484+441+256}{704}[/tex]

[tex]\ \ \sf\longmapsto cosB=\dfrac{1181}{704}[/tex]

[tex]\ \ \sf\longmapsto cosB=0.42[/tex]

[tex]\ \ \sf\longmapsto B=cos^{-1}(0.42)[/tex]

[tex]\ \ \sf\longmapsto B=64.8°[/tex]

Otras preguntas