Mathematics Question and Solution
tan60 = √(3)/a
a = 1 unit.
b = 8-a
b = 7 units.
tanc = √(3)/7
c = atan(√(3)/7)°
d = 2c
d = 2atan(√(3)/7)°
e = 180-60-d
e = (120-2atan(√(3)/7))°
f = ½(e)
f = (60-atan(√(3)/7))°
Calculating R, radius of the bigger circle.
It implies;
tan(60-tan(√(3)/7)) = R/g
g = R/tan(60-atan(√(3)/7)) units.
tan60 = R/h
h = R/tan60 units.
It implies;
g+h = 8
(R/tan(60-atan(√(3)/7)))+(R/tan60) = 8
1.5396007178R = 8
R = 8/1.5396007178
R = 5.1961524227 units.
Again, R is the radius of the bigger circle.
