Calculating length AB.
Let a be the radius of the inscribed semi circle.
b = 180-45
b = 135°
c² = 12²+5²-2*5*12cos45
c = 9.1731775442 units.
d = c+a
d = (9.1731775442+a) units.
e...
Let AB = BC = 1 unit.
tan30 = a/1
a = ⅓√(3) units.
a = 0.5773502692 units.
a is CD.
cos30 = 1/b
b = ⅓(2√(3)) units.
b = 1.1547005384 units.
b is BD.
c = 90-30
c = 60°
c is angle BDC...
Calculating equation of the curve.
(y-12) = a(x-6)²
At x = 0, y = 0
Calculating a.
-12 = a*36
a = -⅓
It implies;
y-12 = -⅓(x-6)²
y = -⅓(x²-12x+36)+12
y = ⅓(-x²+12x-36+36)
y = ⅓(12x-x²)...
Let R be radius of the quarter circle.
Let r be radius of the inscribed circle.
R will be;
√(3²+4²)
R=√(25)
R= 5 unit.
Calculating r, radius of the inscribed circle.
Therefore r will...
Let the base of the equilateral be 1 unit.
a = 180-22-16-38
a = 180-76
a = 104°
(1/sin104) = (b/sin38)
b = 0.6345091075 units.
c = 180-16-44-38
c = 180-98
c = 82°
(1/sin82) = (d/si...
Shaded region/area is;
2(sector area with radius 2cm and angle 60°) - (equilateral triangle area with sides 2cm each side) + (square area with sides 2cm each side) - (square area with sides 4cm...
Sir Mike Ambrose is the author of the question.
Exact Area R in its simplest from will be;
Area semi circle with radius 2 unit - Area right-angled triangle with height 2√(2+√(2)) unit and wid...
a = 5+√(7)-1
a= (4+√(7)) units.
tanb = 1/(4+√(7))
b = atan(1/(4+√(7)))
c = 2b
c = 2atan(1/(4+√(7)))°
cos(2atan(1/(4+√(7)))) = (5+√(7))/d
d = (5+√(7))/cos(2atan(1/(4+√(7))))
d = 8 unit...
Let the three equal lengths of the ascribed pentagon be 1 unit each.
a² = 2-2cos80
a = 1.2855752194 units.
b = ½(180-80)
b = 50°
c = 80-b
c = 30°
d = 90-b
d = 40°
It implies;...
a = ⅛*180(8-2)
a = 135°
a is the single interior angle of the regular octagon.
b² = 2²+2²-2*2*2cos135
b = 3.69551813 units.
c = 135-2*½(180-135)
c = 135-45
c = 90°
d = 90-½(45)
d = 9...
