tana = 1/2
a = atan(1/2)°
b = 180-2a
b = (180-2atan(½))°
Notice!
Radius of the inscribed circle is 1 unit.
Area yellow is;
Area triangle with height 2 units and base 1 unit - Area sq...
Calculating the area of the inscribed square.
a = ½(45)
a = 22.5°
b = ½(180-45)
b = ½(135)
b = 67.5°
cos22.5 = 6/c
c = 6.4943532018 units.
Let d be the side length of the inscribed...
sin30 = a/6
a = 3 units.
b = 6+2a
b = 12 units.
Let the side length of the inscribed regular pentagon be c.
Calculating c.
d² = 2c²-2c²cos108
108° is the single interior angle of the...
Radius of the half circle is 5 units.
5² = 4²+a²
a = 3 cm.
tanb = 4/3
b = atan(4/3)°
c = 2b
c = 2atan(4/3)°
5² = 3²+d²
d = √(25-9)
d = 4 cm.
tane = 3/4
e = atan(3/4)°
f = 2e...
a = 180-2(70)
a = 40°
a is angle ACB.
b = 180-2a
b = 180-80
b = 100°
b is angle AOC.
Let r be the radius of the circle.
Calculating r.
Observing Cosine Rule.
9² = 2r²-2r²cos100...
Calculating r, radius of the circle.
a = (12-r) units.
It implies;
r² = 5²+(12-r)²
r² = 25+144-24r+r²
24r = 169
r = (169/24) units.
r = 7.0416666667 units.
Calculating length AB.
Let a be the radius of the inscribed semi circle.
b = 180-45
b = 135°
c² = 12²+5²-2*5*12cos45
c = 9.1731775442 units.
d = c+a
d = (9.1731775442+a) units.
e...
Let AB = BC = 1 unit.
tan30 = a/1
a = ⅓√(3) units.
a = 0.5773502692 units.
a is CD.
cos30 = 1/b
b = ⅓(2√(3)) units.
b = 1.1547005384 units.
b is BD.
c = 90-30
c = 60°
c is angle BDC...
Calculating equation of the curve.
(y-12) = a(x-6)²
At x = 0, y = 0
Calculating a.
-12 = a*36
a = -⅓
It implies;
y-12 = -⅓(x-6)²
y = -⅓(x²-12x+36)+12
y = ⅓(-x²+12x-36+36)
y = ⅓(12x-x²)...
Let R be radius of the quarter circle.
Let r be radius of the inscribed circle.
R will be;
√(3²+4²)
R=√(25)
R= 5 unit.
Calculating r, radius of the inscribed circle.
Therefore r will...
