The length of segment EF is 12 cmWhich statements regarding triangle DEF are correct? Select three options.

Answer:Therefore the answer is:EF is the longest side of △DEF. DF = 6 cmDE=6√3 Step-by-step explanation:The complete question is in the attached picture:Solution:We have to find DE .sin60 = Perpendicular/Hypotenusesin60 = P/EFsin60 = DE/EF√3/2 = DE/12By cross multiplication:12(√3/2) = DE6√3 = DENow we have to find DFBy applying Pythagorean TheoremP^2 + B^2 = H^2(6√3)^2 + B^2 = (12)^236(3)+B^2 = 144108+B^2 = 144Combine the like terms:B^2 = 144-108B^2 = 36Take square root at both sides√B^2 = √36B= 6cmDF= 6cmTherefore the answer is:EF is the longest side of △DEF. DF = 6 cmDE=6√3