Shaded/Area Blue is;
2(area sector with radius 4 unit and angle (180-2atan(½))° - area triangle with two side 4 unit respectively, and angle (180-2atan(½))°) + 2(area sector with radius 2 unit and...
Sir Mike Ambrose is the author of the question.
Let the square side be 2 units.
Area Square is;
2²
= 4 square units.
Calculating Area Yellow.
(2-a)²+1 = a²+4
4-4a+a²+1=a²+4
a = ¼ unit.
b² = 1+...
Let P be 2^(x)
(P⁹/8192)-256P⁶ = 0
Let y be P³
(y³/8192)-256y² = 0
y³-2097152y² = 0
y = 2097152
P³ = y
P³ = 2097152
P = 128
2^(x) = P
2^(x) = 128
2^(x) = 2^(7)
x = 7
Let AB be 4 units.
Let BC be 3 units.
Area ABCD is;
4*3 = 12 square units.
Calculating Area CEF.
tana = 3/2
a = atan(3/2)°
a is angle AMD.
b = atan(2/3)°
b is angle DEM.
c = (180-atan(3/2))°
c...
Let AB be 4 units.
BC = 6 units.
Let a be the side length of the inscribed square.
Calculating a.
b² = 4²-a²
b = √(16-a²)
It implies;
a = √(16-a²)
6 = 4
Cross Multiply.
4a = 6√(16-a²)
2a = 3√(...
Sir Mike Ambrose is the author of the question.
Radius of the ascribed circle is 13 cm.
a = acos((2*13²-24²)/(2*13²))
a = 134.76027010392°
b = ½(a)
b = 67.38013505196°
c = 40°
d = b - c
d = 27....
Le the side of the regular hexagon be 1 unit.
cosa = 0.5/1
a = 60°
b = 60-36
b = 24°
c = 108-24
c = 84°
Therefore;
The required angle, x is;
½(180-84)
= ½(96)
= 48°
Sir Mike Ambrose is the author of the question.
Let the length of the rectangle be 2 units.
Length AB is:
√(2) units.
a² = 2+1-2√(2)cos75
a = √(4-√(3)) units.
(a) Let Alpha be x.
Calc...
Sir Mike Ambrose is the author of the question.
Let the side of the square be 1 unit.
Area square is;
1²
= 1 square unit.
1 = ½+¼-½(√(2))cosa
½(√(2))cosa = ¾-1
a = acos(-√(2)/4)
a = 110.70481105...
Let the side length of the regular decagon be 1 unit.
a = (180*8)/10
a = 144°
a is a interior angle of the regular decagon.
b = 144-120
b = 24°
c² = 2-2cos24
c = 0.41582338164 units.
d = ½(180-2...
