Mathematics Question and Solution
Calculating Area Green.
Let theta be x.
a = 90-39
a = 51°
x+x+27 = 51
2x = 51-27
2x = 24
x = 12°
b+x+39 = 180
b = 180-39-x
And x = 12°
b = 180-39-12
b = 129°
Let c be the hypotenuse of the ascribed right-angled triangle.
Therefore;
c/sin129 = d/sin12
d = (csin12)/(sin129)
d = 0.26753235702c units.
Calculating c.
½*c*0.26753235702c*sin39 = 26
0.08418178377c² = 26
c² = 308.85541783
c = 17.5742828539 units.
Again, c is the hypotenuse of right-angled triangle.
sin39 = e/c
e = csin39
e = 17.5742828539sin39
e = 11.0598545581 units.
e is the height of the right-angled triangle.
tan12 = f/e
f = etan12
f = 11.0598545581tan12
f = 2.35084465743 units.
f is the base of the inscribed green area.
It implies, area green is;
½*e*f
= 0.5*11.0598545581*2.35084465743
= 13 square units.
