Calculating lengths x plus y.
Calculating y.
y² = 2(10)²
y = √(2(10)²)
y = 10√(2) cm.
y = 14.1421356237 cm.
Calculating x.
sina = 12/20
a = asin(3/5)°
b = ½(a)
b = (0.5asin(3/5))°
Therefore, l...
Let R be 1 unit (radius of the inscribed big circle).
Let a be the ascribed square side length.
Calculating a.
(a-1)² = 1²+(0.5a)²
a²-2a+1 = 1+¼(a²)
4a²-a² = 8a
3a = 8
a = ⅓(8) units.
Again, a is...
(x³)² = (x²)²+x²
x⁶ = x⁴+x²
Dividing through by x²
x⁴ = x²+1
Let p be x²
p² = p+1
p²-p-1 = 0
Resolving the above quadratic equation via completing the square approach to get p.
(p-½)² = 1+(-½)²
(p...
Calculating angle EHB.
Let the side length of the regular pentagon be 1 unit.
Therefore;
AB = BC = CD = DE = AE = 1 unit.
a² = 2-2cos108
a = 1.6180339887 units.
a is BE, the square side...
Let the radius of the circle be r.
Calculating r.
2(½*12r)+(r*r)+2(½*8r) = ½(12+r)(8+r)
(12r)+r²+(8r) = ½(12+r)(8+r)
24r+2r²+16r = 96+20r+r²
40r+2r² = 96+20r+r²
r²+20r-96 = 0
(r+10)² = 96+100
r = -...
Calculating length PQ.
tana = 12/5
a = atan(12/5)
a = 67.380135052°
b = 180-a
b = 180-67.380135052
b = 112.619864948°
c = ½(b)
c = ½(112.619864948)
c = 56.309932474°
tan56.309932474 = r/d
d = r/...
Sir Mike Ambrose is the author of the question.
Let AC = 2 units.
Therefore;
AB = ⅖ unit.
BC = (8/5) unit.
It implies;
Area Blue is;
Area triangle with height ⅖ unit and base 2sin120 units + Ar...
(7/sin60) = (8/sina)
a = 81.7867892983°
b = 120-a
b = 120-81.7867892983
b = 38.2132107017°
(7/sin60) = (c/sin38.2132107017)
c = 5 units.
c is the side length of the regular hexagon.
cos60 = c/d
½...
Observing similar plane shape (right-angled triangle) side length ratios.
3 - 5
a - (4-a)
Cross Multiply.
5a = 3(4-a)
5a = 12-3a
8a = 12
a = (3/2) units.
b = 4-a
b = 4-(3/2)
b = (5/2) units.
c...
