Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Notice;
BC = 2 units.
a = ⅛(180*6)
a = 135°
b = 2+2(2sin45)
b = 4.82842712475 units.
c = b+2
c = 6.82842712475 units.
Let AB be d.
Calculating d.
d² = 6.82842712475²+2²-4*6.82842712475cos135
d = AB = 8.36308110071 units.
(a) (AB/BC)² exactly in decimal is;
(8.36308110071/2)²
= 17.48528137426
= 18095509063163401/1034899506381316 exactly in fraction.
(b) Calculating green area.
e = (2√(2)+2) units.
f = (2√(2)+4) units.
g = atan((2√(2)+2)/(2√(2)+4))
g = 35.26438968275°
h = 135-g
h = 99.73561031725°
i = 180-h
i = 80.26438968275°
j = 2tan35.26438968275
j = 1.41421356237 units.
k = 90-i
k = 9.73561031725°
l = 2tan9.73561031725
l = 0.34314575051 units.
It implies;
Area Green exactly in decimal is;
2(½*2*4.82842712475) - ½*6.82842712475*1.41421356237sin45 - ½*2*0.34314575051
= 9.6568542495 - 3.41421356237 +
0.34314575051
= 6.58578643764 square units exactly in decimal.
It implies;
(a) = 17.48528137426 exactly in decimal.
(b) = 6.58578643764 square units exactly in decimal.
