Calculating angle x.
Let 1 be the base of the ascribed isosceles triangle.
a = 180-39-2(27)
a = 141-54
a = 87°
(1/sin87) = (b/sin(2*27))
b = 0.8101272456 units.
c = 180-27-15-39
c =...
Let AB be a.
b = (a-2) units.
c = ½(a) units.
c is BD.
d = c-2
d = ½(a)-2
d = ½(a-4) units.
It implies;
2 - (a-2)
½(a-4) - 2
Cross Multiply.
4 = ½(a-4)(a-2)
8 = a²-6a+8
a...
Let 1 be the side length of the ascribed regular hexagon.
a = ⅙*180(6-2)
a = 120°
a is the single interior angle of the ascribed regular hexagon.
b² = 1²+1²-2*1*1cos120
b = 1.7320508076 un...
Calculating Alpha.
Let it be a.
Let b be the radius of the ascribed quarter circle.
c = (b-√(2)) units.
d = (b-2√(2)) units.
It implies, observing similar plane shape (right-angled)...
Calculating angle x.
Let AR be 1 unit.
a = 180-24-15
a = 180-39
a = 141°
a is angle ARK.
(1/sin15) = (b/sin141)
b = 2.4315072749 units.
b is AK.
c = 180-12-6
c = 180-18
c = 162°...
Sir Mike Ambrose is the author of the question.
Calculating the equation of the curve.
y-b=a(x-4)² ----- (1)
At coordinate (8, 0)
-b=16a
Therefore;
a = -b/16
Sub. a in (1) to get...
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 units.
b = 90-18...
Let the side of the inscribed square be a.
Calculating a.
a+2√(a²-(a/2)²) = 10√(2)
a+2√(3a²/4) = 10√(2)
2√(3a²/4) = 10√(2)-a
3a² = 200-20√(2)a+a²
2a²+20√(2)a-200 = 0
a²+10√(2)a-100 = 0...
Sir Mike Ambrose is the author of the question.
Biggest square side is 14 units.
Bigger square side is 8 units.
a = atan(9/16)
(9/16) = b/c
c = (16b/9) units.
(16b/9)+6 = 14
(16b/9)...
Sir Mike Ambrose is the author of the question.
Area Red Total in 1 d. p. Square unit is;
Area Square with side 2√(2) units - Area triangle with height 2√(2) units and base 1.1313708499 units +...
