Mathematics Question and Solution
Calculating Green Inscribed Triangle.
tana = 12/10
a = atan(6/5)°
b = (180-atan(6/5))
b = (90+atan(⅚))°
c² = 10²+12²
c = √(244)
c = 2√(61) cm.
d = (2√(61)-x) units.
It implies;
2(2√(61)-x)sin(90+atan(⅚)) = ½*12xsin(atan(6/5))
24-1.53644255919x = 4.60932767758x
24 = 6.14577023677x
x = 3.90512483796 cm.
It implies;
2A = 0.5*3.90512483796*12sin(atan(6/5))
Where 2A is area green.
2A = 18 cm²
It implies;
A = 9 cm²
Green area is;
½(2+12)*12-18-9
= 84-27
= 57 cm²
