Mathematics Question and Solution
a² = 15²+12²-2*12*15cos120
a = 23.43074902772 cm.
Where a is the side length of the equilateral triangle ABC.
(23.43074902772/sin120) = (12/sinb)
b = 26.32950349168°
c = 60-b
c = 33.67049650832°
d² = 15²+15²-2*15*15cos120
d = 25.98076211353 cm.
e = atan(7.5/25.98076211353)
e = 16.10211375199°
f = 90-e
f = 73.89788624801°
g = 180-f-c
g = 72.43161724367°
(15/sin72.43161724367) = (h/sin73.89788624801)
h = 15.11661227595 cm.
i = a-h
i = 8.31413675177 cm.
Let the radius of the green inscribed circle be r.
Calculating r.
(r/tan30)+(r/tan(0.5*72.43161724367) = 8.31413675177
r = 2.68406898148 cm.
Are Green in cm² to 2 decimal places is;
π(2.68406898148)²
= 22.63274441053 cm²
≈ 22.63 cm²
