Mathematics Question and Solution
Calculating Length EF.
Let x be EC = CH, radius of the small inscribed circle.
a = (20-x) cm.
tanb = 10/20
b = atan(½)°
c = ½(90-2atan(½))
c = ½(atan(2)-atan(½))
c = 18.4349488229°
Calculating x, radius of the small inscribed circle.
tan18.4349488229 = x/(20-x)
20tan18.4349488229-xtan18.4349488229 = x
x+xtan18.4349488229 = 20tan18.4349488229
x = (20tan18.4349488229)÷(1+tan18.4349488229)
x = 5 cm.
d² = 5²+20²
d = 5√(17) cm.
d = 20.6155281281 cm.
tane = 5/20
e = atan(¼)°
f = 90-2atan(½)-atan(¼)
f = 22.8336541779°
It implies, length EF is;
Let it be g.
g² = 20²+20.6155281281²-2*20*20.6155281281cos22.8336541779
g = √(65) cm.
g = 8.0622577483 cm.
Again, g is length EF.
