Triangle DEF is equilateral. Find AE.
DA = 3, AF = 2
DE = DF = DA + AF = 5
Law of Cosines
AE^2 = DA^2 + DE^2 - 2 (DA * DE)cos (60 degrees)
AE^2 = 3^2 + 5^2 - 2 ( 3 * 5) (1/2)
AE^2 = 19
AE = sqrt (19) ≈ 4.36