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Let the two equal lengths be 1 unit.
(a) Calculating Theta exactly.
Let theta be x.
Calculating x.
x = ½(90-54)
x = ½(36)
x = 18°
sin18 = a/1
a = 0.30901699437 unit.
b = 90-18
b = 72°
sin72 =...
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Radius of the semi circle is 5 units.
Calculating r, radius of the inscribed circle.
(5-r)² = 3²+r²
25-10r+r² = 9+r²
10r = 16
r = ⅕(8) units.
a = 3-r
a = ⅕(7) units.
b² = 5²-a²
b = ⅕(24) units....
AE = CF = (12√(2)-12) cm.
AE = CF = 4.97056274848 cm.
EF = 12√(2)-2(4.97056274848)
EF = 7.02943725152 cm.
sin60 = a/7.02943725152
a = 6.08767123412 cm.
a = height of triangle EFG.
It implies;
L...
Let AB be 1 unit.
(1/sin150) = (a/sin20)
a = 0.68404028665 units.
a is AD.
Notice;
AB = AC = 1 unit.
(CD)² = 1+0.68404028665²-2*0.68404028665cos30
CD = 0.53208888624 units.
Therefore, the requi...
Let the radius of the green circle be r.
sina = (3+2√(3))/(6+4√(3))
a = asin(½)
a = 30°
It implies;
cos30 = (3+2√(3))/((3+2√(3))+r)
6+4√(3) = 3√(3)+6+√(3)r
√(3) = √(3)r
r = 1 unit.
(3/sin108) = (EG/sin18)
EG = 0.9747590887 units.
(3/sin108) = (EF/sin54)
EF = 2.55195242506 units.
AF = 4-2.55195242506
AF = 1.44804757494 units.
sin18 = a/1.44804757494
a = 0.44747130932 units....
Let the height and base of the rectangle be x and y respectively.
Let the inscribed circle's radius be r.
Therefore;
0.5xy = 36
xy = 72 square units.
Therefore;
y = 72/x --- (1)....
Let the radius of the large circle be 1 unit.
Diameter of the large circle = 2 units.
sin60 = 2/a
a = ⅓(4√(3)) units.
Where a is the side length of triangle ABC.
b² = 2-2cos
b = √(3) units.
c =...
