Sir Mike Ambrose is the author of the question.
Let the square side be x.
Calculating x.
25 = (x²-9)+2x²-2√(2)x*√(x²-9)cos(45+y)
Where y is an angle.
Notice;
cosy = √(x²-9)/x and siny = 3/x.
It...
100 = 49+64-2*7*8cosA
112cosA = 113-100
A = acos(13/112)
A = 83.3345727438°
(7/cosB) = (10/cos83.3345727438)
B = 44.0486256741°
(8/cosC) = (10/cos83.3345727438)
C = 52.6168015821°
a²=...
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Let the square side be 1 unit.
Area Square is;
1² = 1 square unit.
Calculating Area Blue.
a = 108-60-36
a = 12°
b = 180-12-108
b = 60°
1 = 2c²-2c²cos108
1 = 2.6180339887c²
c = 0.6180339887 unit...
Let the side length of the regular pentagon be 1 unit.
a = ½(108)-25
a = 54-25
a = 29°
b = 72-29
b = 43°
(c/sin108) = (1/sin43)
c = 1.3945143742 units.
tan25 = d/1.3945143742
d = 0....
Let the regular hexagon side length be a.
Calculating a.
0.5a²sin120 = 4√(3)
√(3)a² = 16√(3)
a = 4 units.
b² = 4²+4²-2*4*4cos120
b = 4√(3) units.
c = ½(b)
c = 2√(3) units.
d² = 2²+4²-2*2*4cos12...
a² = 6²+18²-2*6*18cos150
a = 23.3893455919 cm.
(23.3893455919/sin150) = (18/sinb)
b = 22.6307402124°
tan22.6307402124 = c/6
c = 2.5013366786 cm.
Area Red exactly in decimal is;
0.5*2.5013366786*...
Sir Mike Ambrose is the author of the question.
Let the single side length of the congruent regular hexagons be 1 unit.
Therefore;
Area red is;
Area trapezium with two parallel side length ½(3√(...
sin30 = a/10
a = 5 cm.
b = 10+2a
b = 20 cm.
c² = 20²+4²-160cos60
c = 4√(21) cm.
c = 18.3303027798 cm.
(18.3303027798/sin60) = (20/sind)
d = asin(5√(7)/14)°
d = 70.8933946491°
e = 180-d
e = (180-...
Sir Mike Ambrose is the author of the question.
Let the side of square ABCD be x.
Calculating x.
½*x(x+½(x)) = 84+24
½(½(3x²)) = 108
¼(x²) = 36
x² = 36*4
x = 12 cm.
Notice;
The base of blue area...
