22statonj 22statonj
  • 28-02-2021
  • Mathematics
contestada

In ∆DEF, DE = 18, EF = 16, and DF = 12. Find m∠F.

Respuesta :

cairde
cairde cairde
  • 28-02-2021

Answer:

∠F=78.58484226°

Step-by-step explanation:

a²=b²+c² - 2bc cosA

DE²=EF²+DF² - 2(EF)(DF)cos∠F

18²=16²+12²-2(16)(12)cos∠F

324=256+144-384cos∠F

324-400=-384cos∠F

76=384cos∠F

0.197916=cos∠F

∠F=cos⁻¹(0.197916)

∠F=78.58484226°

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