Question

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

Answer 1

∠F=78.58484226°

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°