Mathematics Question and Solution
Calculating Triangle ADE.
a² = (3√(3))²+(4√(3))².
a² = 27+48
a = √(75)
a = 5√(3) units.
a is AC.
3√(3)b+4√(3)b+5√(3)b = 3√(3)*4√(3)
12√(3)b = 36.
√(3)b = 3
b = √(3) units.
b is the radius of the inscribed circle.
c = 3√(3)-b
c = 2√(3) units.
d = a-c
d = 5√(3)-2√(3)
d = 3√(3) units.
tane = 3√(3)/√(3)
e = atan(3)°
f = ½(180-atan(3))
f = 54.2174744115°
f is half angle CDE.
g = ½(270-atan(4/3)-(180-atan(3)))
g = 54.2174744115°
g is half angle BED.
Notice.
Angle CDE = Angle BED.
Therefore AE = AD.
tan54.2174744115 = √(3)/h
h = 1.24839158916 units.
j = 4√(3)-√(3)-h
j = 3√(3)-1.24839158916
j = 3.94776083355 units.
j is AE = AD.
tank = 3√(3)/4√(3)
k = atan(3/4)°
It implies, area triangle ADE is;
0.5*3.94776083355*3.94776083355sin(atan(3/4))
= 4.67544467967 square units.
