Mathematics Question and Solution
a = asin(1/3)°
a = 19.47122063449°
a = angle ABF.
Let the centre of the diameter of the half circle be O.
Angle AOF = 90-19.47122063449 = 70.52877936551°
(OC)² = 12²+18²
OC = 6√(13) cm.
Angle COE = acos(1/√(13)) = 73.89788624801°
Angle BOC = atan(2/3) = 33.69006752598°
It implies;
Angle EOF will be;
73.89788624801-(70.52877936551-33.69006752598)
= 37.05917440848°
Therefore;
Length EF is;
(EF)² = 6²+6²-2*6*6cos37.05917440848
EF = 3.81353187415 cm.
