0.5*a*6sin75 = 9
a = 9/(3sin75)
a = 3/sin75
a = 3.1058285412 units.
a is AB.
b² = 3.1058285412²+6²-2*3.1058285412*6cos75
b = 6 units.
b is AC.
It implies, triangle ABC is isosceles....
Calculating length CD.
Notice!
The composite plane shape is not drawn to scale.
tan60 = 8/a
a = 8/√(3)
a = ⅓(8√(3)) units.
a is OE.
(⅓(8√(3)))²+8² = b²
b² = ⅓(64)+64
b² = ⅓(64+192)
b²...
Let the square side length be 2 units.
Therefore, r, radius of the circle is;
r = 1 unit.
Calculating the required angle, let it be a.
cosb = 1/2
b = acos(1/2)
b = 60°
c² = 2²+2²
c...
Notice!
The side length of the inscribed biggest square is 5 units.
Calculating inscribed red area.
tana = 2.5/5
a = atan(½)°
b = 2atan(½)°
tanc = 5/2.5
c = atan(2)°
d = 2atan(2)°...
Let the side length of the three equal regular triangles be 2a units each.
b² = 2a²-2a²cos120
b = √(3)a unit.
(6√(7))² = (2a)²+(√(3)a)²-2*2a*√(3)acos90
252 = 4a²+3a²
252 = 7a²
a² = 36
a...
Sir Mike Ambrose is the author of the question.
Area R ÷ Area Square exactly in its simplest decimal form is;
Area R is;
½(5x7.5) - ½(√(81.25)x√(65.25))sin(tan–¹(5/7.5) - tan–¹(3/7.5)) - ½((4....
Sir Mike Ambrose is the author of the question.
Let the square side be 1 unit.
Therefore;
Area B is;
Area triangle with height 1 unit and base sin(53.13010235416) unit - Area triangle with...
a*9 = 6*3
a = 2 units.
b = ½(9+2)
b = 5.5 units.
c = ½(6+3)
c = 4.5 units.
d = c-3
d = 1.5 units.
Calculating e, radius of the circle.
e² = b²+d²
e² = 5.5²+1.5²
e = 5.70087712...
a²+8² = 10²
a = 6 units.
b = ½(10)
b = 5 units.
b is the radius of the ascribed semi circle.
6² = 5²+5²-2*5*5cosc
50cosc = 50-36
cosc = 14/50
c = acos(7/25)°
c = 73.7397952917°
d =...
a² = 24²+7²
a = 25 units.
a is AC.
b = 7+a
b = 32 units.
c² = b²+24²
c = √(32²+24²)
c = 40 units.
c is the diameter of twice the quarter circle (semi circle (2AB)).
d = ½(c)
d = 20...
