Sir Mike Ambrose is the author of the question.
sin30 = a/12
a = 6 cm.
sin60 = b/12
b = 6√(3) cm.
Let the inscribed square side be c.
Calculating c.
(c/sin60)+(csin30) = 6
(⅓(2√(3))+½)c = 6
⅙(4...
Let the two congruent square side be 1 unit.
a = √(2) units
a is a diagonal of one of the congruent squares.
tanb = 1/(√(2)+1)
b = 22.5°
c = 90-b
c = 67.5°
d = ½(180-135)
d = ½(45)
d = 22.5°
e...
Calculating a, side length of the regular hexagon.
Notice;
Red Area is 122 square units.
sin30 = b/a
b = (a/2) units.
c = a+2b
c = 2a units.
sin60 = d/a
d = (√(3)a/2) units.
It implies;
122+0....
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Let AB be 2 units.
Therefore;
BC = 1 unit.
tan30 = a/3
a = √(3) units.
tan30 = b/1
b = ⅓(√(3)) units.
c = a-b
c = ⅔(√(3)) units.
d² = (⅓√(3))²+1²
d = ⅔(√(3)) units.
sin60 = ⅔*√(3)/e
e = ⅓(4)...
Let AB be 1 unit.
Therefore;
BC = 2 units.
It implies, the regular hexagon side length is 3 units.
a = 120-108
a = 12°
b² = 2²+3²-2*2*3cos12
b = 1.1234895599 units.
(1.1234895599/sin12) = (2/s...
Sir Mike Ambrose is the author of the question.
a = 4/2tan(180/9)
a = 2/tan20 units.
b = 4/2tan(180/6)
b = 2/tan30 units.
Therefore;
Red Length is;
a+b
= (2/tan20)+(2/tan30)
= 2(tan...
Sir Mike Ambrose is the author of the question.
Let r be the radius of the three congruent circles.
Calculating r.
(9+r)² = (9-r)²+(9-3r)²
81+18r+r² = 81-18r+r²+81-54r+9r²
36r = 81-54r+9r²
9r²-90r...
a = 6-2
a = 4 units.
b² = 6²-4²
b = 2√(5) units.
c = 6-b
c = (6-2√(5)) units.
d = asin(⅔)°
tan(asin⅔) = e/(6-2√(5))
e = ⅕(12√(5)-20) units.
f = 4+e
f = ⅕(12√(5)) units.
g² = 6²+(⅕(12√(5)))²
g...
Let AB be 1 unit.
a² = 2-2cos108
a = 1.61803398875 units.
a is BE.
(1.61803398875/sin156) = (b/sin6)
b = 0.41582338164 units.
b is BP.
(1.61803398875/sin156) = (c/sin18)
c = 1.22929666779 units....
