Let the two equal lengths be 1 unit.
a = 180-20-80
a = 80°
(1/sin20) = (b/sin80)
b = 2.8793852416 units.
c = 2.8793852416-1
c = 1.8793852416 units.
d² = 1.8793852416²+1²-2*1.8793852416cos80
d =...
Calculating angle BCD.
Let AC = 2 units.
Therefore;
AB = BC = 1 unit.
a = 60-45
a = 15°
a is angle ADB.
It implies;
(1/sin15) = (b/sin30)
b = 1.9318516526 units.
b is BD.
1.9318516526² = 2c²
c...
Calculating area shaded.
tana = 2/4
a = atan(½)°
b = 180-2a
b = (180-2atan(½))°
c = 180-b
c = 180-(180-2atan(½))
c = 2atan(½)°
Notice.
Radius of the inscribed half circle r, is;
r = ½(4)
r = 2...
Sir Mike Ambrose is the author of the question.
Yellow area exactly in decimal cm² is;
Area triangle with height 7.49903313849 cm and base 8sin(32.2356103172) cm + Area triangle with height 7.49903...
1. The proof that triangle EGH is equilateral.
Let the side length of the regular hexagon be 1 unit.
a = ⅙(180(6-2))
a = 30*4
a = 120°
a is single interior angle of the regular hexagon.
b² = 1²+0...
a² = (2r)²+r²
a² = 5r²
a = √(5)r units.
a is BD.
Where r is the radius of the circle.
b = ½(a)
b = ½(√(5)r) units because BD, points B and D are symmetry with respect to length AC.
tanc = 2r/r
c =...
Let the side length of the regular octagon be 1 unit.
a = ⅛(180(8-2))
a = ⅛(180*6)
a = 3*45
a = 135°
a is the single interior angle of the regular octagon.
b = ½(360-135-135)
b = ½(360-270)
b = ½(...
Sir Mike Ambrose is the author of the question.
Area ABC (yellow area) exactly is;
Area triangle with height ⅓√(265) cm and base ((5√(26)/6)sin84.3306169587) cm.
= ½*⅓√(265)*((5√(26)/6)sin84...
Calculating angle BAC, an interior angle of the inscribed triangle ABC.
0.5*15*18sinx = Area triangle ABC
135sina = 81
sinx = (81/135)
x = asin(81/135)
x = 36.8698976458°
x again, is angle BAC.
a²...
Let BF = CF be a.
It implies;
BC = 2a
BC is the side length of the regular pentagon.
Calculating a.
b = ⅕(180(5-2))-90
b = 108-90
b = 18°
b is angle BFG
Notice.
108° is the single interior angl...
