The radius of the inscribed circle is 2 units.
a = 2atan(⅓)°
b = 2atan(⅕)°
c = 180-a-b
c = (180-2atan(⅓)-2atan(⅕))°
sin(2atan(⅓)) = d/16
d = (48/5) units.
cos(2atan(⅓)) = e/16
e =...
8 = 4
a = (8-a) Cross multiply.
64-8a = 4a
64 = 12a
a = ⅓(16) cm.
b = 8-a
b = ⅓(8) cm.
c = atan(⅔)°
d = atan(3/2)°
⅔ = 8/e
e = 12 cm
⅔ = f/8
f = ⅓(16) cm.
g = 8-f
g = ⅓(...
Let the side of the green square be x.
Therefore;
x/(tan(atan¾)) + x + x/(tan(atan(4/3))) = 5
⅓(4x) + x + ¼(3x) = 5
16x + 12x + 9x = 60
37x = 60
x = (60/37) units.
It implies;
Area square green...
Let AC be 1 unit.
Area smaller pentagon is;
½(5)*(1/(2tan(36)))
= 1.72047740059 square units.
a² = 1²+0.5²-cos108
a = 1.24860602048 units.
Where a is CD.
(1.24860602048/sin108) =...
a² = 10²+16²-2*10*16cos120
a = 2√(129) units.
Where a is length AC.
(3√(129)/sin120) = (16/sinb)
b = 37.58908946897°
c = 90-b
c = 52.41091053103°
d = 60-b
d = 22.41091053103°
e...
Sir Mike Ambrose is the author of the question.
y = 2^(x)
P coordinate is;
P(1, 2)
dy/dx = 2^(x)In2
For x = 1
dy/dx = 2In2
It implies;
Q coordinate is;
Q(0, (2-2In2))
Th...
Let the two congruent lengths be 1 unit.
tan40 = a/1
a = 0.83909963118 unit.
cos40 = 1/b
b = 1.30540728933 units.
Calculating r, radius of the red inscribed circle.
(r/tan(20)) + (r/t...
Let the side of the regular pentagon be 1 unit.
Calculating Area Red.
a² = 1²+1²-2*1*1cos108
a = 1.61803398875 units.
b = 108-36-60
b = 12°
(c/sin12) = (1.61803398875/sin96)
c = 0.3382...
a² = 15²+12²-2*12*15cos120
a = 23.43074902772 cm.
Where a is the side length of the equilateral triangle ABC.
(23.43074902772/sin120) = (12/sinb)
b = 26.32950349168°
c = 60-b
c = 33.67...
