Answer:
EF is the longest side of △DEF.
DF = 6 cm
DE = 6√3cm
Step-by-step explanation:
The question lacks options. Here are the options.
EF is the longest side of △DEF.
DF = 6 cm
DE = 12 StartRoot 3 EndRoot cm
DF = 4 StartRoot 3 EndRoot cm
DE = 6 StartRoot 3 EndRoot cm
The right angle triangle has 3 sides namely the hypotenuse (longest side) and the other two sides which are opposite and adjacent.
Given angle D E F to be 30 degrees, the side facing this angle will be DF which will serve as the opposite.
Using SOH, CAH, TOA,
Sin<DEF = Opp/Hyp = DF/EF
Given <DEF = 30° and EF = 12cm(hyp)
Sin30° = DF/12
DF = 12sin30°
DF = 12(0.5)
DF = 6 cm
DE will be the third side which is the adjacent side. According to CAH;
Cos<DEF = adj/hyp = DE/EF
Cos30° = DE/12
DE = 12cos30°
DE = 12× √3/2
DE = 6√3 cm
Based on the calculation, the following are true:
EF is the longest side of △DEF.
DF = 6 cm
DE = 6√3cm
