First draw a triangle, with D at the top, E at bottom left and F at bottom right.
Dropping the perpendicular bisector from D, to length FE.
Angle D/2 = 75/2 = 37.5 degrees.
Let the bisector meet FE at G.
FE = FG + GE.
Sine 37.5 = (GE)/5 Cross Multiplying.
GE = 5Sin37.5.
But FE = Twice GE
FE = 2*(5Sin37.5) = 10Sin37.5 Evaluate with your calculator.
FE = 6.08
b) Measure of Angle F.
F is one of the base angles of the isosceles triangle and base angles are equal.
Let Angles of the Isosceles triangle be x, x, 75.
x + x + 75 = 180 Sum of angles in a triangle.
2x + 75 = 180.
2x = 180 -75
2x = 105. Divide by 2.
x = 105/2 = 52.5
Therefore angle F = 52.5 degrees.
c) Angle E = Angle F.
Angle E = 52.5 degrees.
Cheers.
