Mathematics Question and Solution
Notice.
The composite plan shape is not drawn to scale.
Calculating the inscribed orange triangle area.
Notice Again.
3 units is the diameter of the inscribed circle.
a = ½(3)
a = 1.5 units.
a is the radius of the inscribed circle.
tanb = 3/4
b = atan(3/4)°
tan(atan(¾)) = c/1.5
¾ = ⅓(2c)
c = 9/8 units.
d = (3/2)-(9/8)
d = 3/8 units.
e = (180-atan(4/3))°
e = 126.869897646°
(1.5/sin(180-atan(4/3))) = ((3/8)/sinf)
f = 11.5369590328°
g = 180-2f
g = 156.926081934°
h² = 2*1.5²-2*1.5²cos156.926081934
h = 2.93938769134 units.
j = 180-(180-atan(4/3))-11.5369590328
j = 41.5931433214°
(k/sin41.5931433214) = ((3/8)/sin11.5369590328)
k = 1.24469384567 units.
l = 180-41.5931433214
l = 138.406856679°
m² = 2*1.5²-2*1.5²cos138.406856679
m = 2.80454076851 units.
n = 0.5(180-138.406856679)
n = 20.7965716605°
o = f+n
o = 11.5369590328+20.7965716605
o = 32.3335306933°
It implies, area orange inscribed triangle is;
0.5*h*m(cos32.3335306933)
= 0.5*2.93938769134*2.80454076851cos32.3335306933
= 3.48272446112 square units.
