a² = 8-8cos(360-90-108)
a² = 8-8cos162
a = 3.9507533624 units.
b = ½(180-162)
b = 9°
c = 90+9
c = 99°
d² = 3.9507533624²+1-2*3.9507533624cos99
d = 4.2242774658 units.
(4.2242774658/sin99) = (3.9...
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Notice;
Red circle and black circle are congruent, they have equal radius, 1 cm.
Calculating Area Shaded.
a = 60-45
a = 15°
It implies;
Area Shaded is;
Area sector with radius 1 cm...
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Let AB be x.
Therefore BC = 2x.
Calculating x.
Yellow area + Area triangle with height 2x and base ½(3x)sin60 = Area trapezoid with two parallel side ½(3x) and 2x, and height ½(3√(3)x).
Therefore;...
Area blue exactly in cm² decimal is;
Area trapezoid with two parallel sides 12 unit and (12-16tan15) unit, and height 16 unit - Area triangle with height (12-16tan15) unit and base 4 unit - Area tr...
Notice;
cos2x = 1-2(sinx)² --- (1).
Substituting (1) in the given equation.
½(3-6(sinx)²+3)+4sinx+1 = 0
3-6(sinx)²+3+8sinx+2 = 0
6(sinx)²-8sinx-8 = 0
Calculating sinx.
Let sinx be p.
6p²-8p-8 =...
sinxcos60+sin60cosx-(cosxcos45+sinxsin45) = 0
0.5sinx+½(√(3)cosx)-½(√(2)cosx)-½(√(2)sinx) = 0
0.5sinx-½(√(2)sinx) = ½(√(2)cosx)-½(√(3)cosx)
sinx(1-√(2)) = cosx(√(2)-√(3))
sinx = ((√(2)-√...
Sir Mike Ambrose is the author of the question.
Let the side length of the regular pentagon be 2 unit.
Therefore the angle theta is;
asin(2sin42÷1.65418183057)
= 54°
Area green is;
Area...
Calculating yA.
Notice;
xA = 4
And y = (16+e^(0.5x))/4
y = ¼(16+e²)
Where y is yA.
Therefore;
Shaded Area as a single fraction is;
Area Rectangle with width 4 units and length ¼(16+e²) units - A...
