ED = 3.8(tan 40°) (option A)
ED = 3.8/tan 50° (option D)
Step-by-step explanation:
opposite = side opposite the angle 40° = DE
hypotenuse = EF = 5
adjacent = DF = 3.8
Since we are looking for DE, we can apply the sine ratio (SOH) or the tangent ratio (TOA)
The options are in tan, so we would focus on this.
tan 40° = opposite/adjacent
tan 40° = ED/3.8
ED = 3.8(tan 40°) (option A)
Since we have 40 degree as angle F, it means the third angle is 50 degree. This because 90- 40 = 50°. The 50°is angle E.
Using the angle as 50°:
opposite becomes = 3.8 as this is the side facing 50°
adjacent = ED
tan 50° = opposite/ adjacent
tan 50°= 3.8/ED
ED = 3.8/tan 50° (option D)