Let the two congruent longer lengths be 1 unit.
(1/sin135) = (b/sin30)
b = 0.70710678119 units.
(1/sin135) = (c/sin15)
c = 0.36602540378 units.
d = 1+b
d = 1.70710678119 units.
e = 1+c
e = 1.366...
Let the longer pair of congruent lengths be 1 unit.
(1/sin60) = (a/sin20)
a = 0.39493084363 units.
(1/sin60) = (b/sin100)
b = 1.1371580426 units.
c = 1+a
c = 1.39493084363 units.
d = 1+b
d = 2.1...
Let the side length of the regular hexagon be 1 unit.
sin60 = a/1
a = ½√(3) units.
tanb = (a/1)
b = atan(0.5√(3))°
b = 40.89339464913°
b is angle DEH.
c = atan(2/√(3))
c = 49.10660535087°
d = 12...
Let r be the radius of the inscribed circle.
Calculating r.
a = √(2*24²)
a = 24√(2) units.
b = √(2*r²)
b = √(2)r units.
It implies;
16+r+√(2)r = 24√(2)
r(√(2)+1) = (24√(2)-16)
r = (24√(2)-16)/(...
Let angle BAC = 30°
Let AB = AC = 1 unit.
a² = 2-2cos30
a = 0.51763809021 units.
a is BC.
Since;
BK = 2CK, therefore;
3CK = BC
CK = 0.51763809021/3
CK = 0.17254603007 units.
It impli...
Sir Mike Ambrose is the author of the question.
Let the side length of the inscribed regular hexagon be 1 unit.
Calculating r, radius of the circle.
1+2(sin30)
r = 2 units.
Area circle is;
π(2)²...
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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