Calculating the width of the ascribed rectangle.
a = 180-60-x
a = (120-x)°
Let b be the side length of the inscribed regular triangle.
cosx = 1/b --- (1).
At (1).
1 is adjacent.
b...
Calculating Perimeter of the ascribed Hexagon.
a = ⅙*180(6-2)
a = 120°
Let x be the side length of the regular hexagon.
b² = 2x²-2x²cos120
b = √(3)x units.
sin30 = c/x
c = ½(x) units...
Sir Mike Ambrose is the author of the question.
Calculating
Area R ÷ Area S Exactly.
Calculating the equation of the curve.
y-b=a(x-4)² ----- (1)
At coordinate (8, 0)
-b=16a
Therefore;
a = -b...
Calculating r, radius of the circle.
It implies;
(45+15)*15 = 20*a
a = 45 cm.
b = 20+a
b = 65 cm.
c² = 45²+65²
c = 25√(10) cm.
c = 79.0569415042 cm.
c is the diameter of the circle...
Sir Mike Ambrose is the author of the question.
Area Blue, in cm² to 1 d. p. is;
Half area regular pentagon with side 12 cm - area triangle with height 6 cm and base 6tan24 cm - area triangle w...
Calculating x, length DF.
Let a be the radius of the ascribed half circle.
b = (a-6) units.
c = (a-7) units.
7² = 6²+8²-2*6*8cosd
96cosd = 36+64-49
d = acos((36+64-49)/96)
d = 57.910...
Calculating the chord length.
Let x be the radius of the half circle.
a = (x-4) units.
b = (x-9) units.
c = (x-7) units.
d = a+b
d = (x-4)+(x-9)
d = (2x-13) units.
d is the length...
Area Orangle ÷ Area Large Square to 3 d. p.
Let the side length of the large square be x.
Calculating x.
25=x²+64-(16xcos20)
Therefore;
x = 11.70244 cm
It implies;
Area large square is;
11.7...
Calculating R, radius of the circle.
(4√(2))² = 1+5²-2*5cosa
32 = 26-10cosa
16 = 13-5cosa
cosa = (-3/5)
a = 126.869897646°
b = 360-2a
b = 360-2*126.869897646
b = 106.260204708°
c = ½...
Calculating r, radius of the circle.
Let theta be x.
Notice.
BC = CD, let it be a.
a² = 2²+13²-2*2*13cosx
a² = 173-52cosx --- (1).
a² = 11²+13²-2*11*13cosx
a² = 290-286cosx --- (2)...
