Let BC be 1 unit.
a = 180-57-49-33
a = 180-139
a = 41°
a is angle BDC.
Observing Sine Rule.
(1/sin41) = (b/sin(49+33))
b = 1.5094191604 units.
b is BD.
c = 180-33-30-41
c = 180-104
c = 76°
c is a...
Sir Mike Ambrose is the author of the question.
Area Green exactly is;
Area trapezoid with parallel sides 3 cm and (6-2√(3)) cm, and height (6-3√(3)) cm.
= ½(6-3√(3))(3+(6-2√(3)))
= ½(6-3√(3))(9-...
Let AB = 1 unit.
Calculating CD.
a = 180-40-60
a = 80°
a is angle ADB.
Observing Sine Rule.
(1/sin80) = (b/sin40)
b = 0.6527036447 units.
b is AD.
c = 180-80
c = 100°
c is angle ADC.
d = 180-1...
Calculating R, radius of the circle.
5² = (½(8))²+a²
25 = 16+a²
a = √(25-16)
a = 3 units.
b = (R-3) units.
Therefore, R is;
R² = (R-3)²+(½(8))²
R² = (R-3)²+4²
R² = R²-6R+9+16
6R = 25...
Calculating R, radius of the ascribed circle.
a² = 4.5²+2.9²-2*4.5*2.9cos60.8
a = 3.9908473908 units.
(3.9908473908/sin60.8) = (4.5/sinb)
b = 79.8304370724°
c = ½(4.5)
c = 2.25 units.
Therefore,...
Calculating area red.
tana = 3/5
a = atan(3/5)°
b = 2a
b = 2atan(3/5)°
tanc = 5/3
c = atan(5/3)°
d = 2c
d = 2atan(5/3)°
Therefore, red area is;
2(area circle with radius 5 units) - 4(area quar...
Let a be the side of the inscribed square.
24² = a²+(2a)²
576 = a²+4a²
576 = 5a²
a = √(576/5)
a = 10.733126292 cm.
b = ½(24-10.733126292)
b = 6.633436854 cm.
b = AM = DR.
c = atan(6.633436854/(...
tana = 3/4
a = atan(3/4)°
b = atan(4/3)°
sin(atan(3/4)) = c/4
c = 2.4 units.
Area Blue is;
Area semi circle with radius 2.5 units - Area sector with radius 2 units and angle (180-2atan(3/4))° +...
tan30 = 4/a
a = 4√(3) units.
sin30 = 4/b
b = 8 units.
c = b-2
c = 8-2
c = 6 units.
Therefore, Area Blue is;
Area semi circle with radius 4 units - Area sector with radius 2√(3) units a...
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