Calculating angle x.
tana = ⅗
a = atan(⅗)°
tan = ⅘
b = atan(⅘)°
c = atan(5/4)°
Therefore, the required angle x is;
x = a+c
x = atan(⅗)+atan(5/4)
x = (atan(⅗)+atan(5/4))°
x = 82....
Calculating the radius of the small inscribed pink circle. Let it be r.
b = ⅕*180(5-2)
b = 108°
b is the single interior angle of the ascribed regular pentagon.
c² = 10²+10²-2*10*10cos108...
Notice!
The ascribed polygon is a regular dodecagon (12 sides and 12 interior angles equal).
It's since interior angle is;
a = 180(12-2)/12
a = 1800/12
a = 150°
The middle inscribed polyg...
Calculating x.
Notice!
Diameter of the ascribed circle is 10 cm.
It's radius, a is;
a = ½(10)
a = 5 cm.
Let b be the radius of the inscribed circle.
c = b-4
c = 1 cm.
d = (5-b) c...
a = 2*135
a = 270°
a is reflex angle BOE.
b = 360-a
b = 90°
b is angle BOE.
c² = 6²+2-2*6√(2)cos135
c = 7.0710678119 units.
c = 5√(2) units.
c is BE.
Notice!
Since angle BOE is 9...
Let a be the radius of the quarter circle.
b = (a-10) units.
b is the width of the inscribed rectangle.
c = (a-5) units.
c is the length of the inscribed rectangle.
Therefore;
a² = (a...
a = 2+2
a = 4 units.
b = a-½(2)
b = 4-1
b = 3 units.
c² = 2(3²)
c = √(18)
c = 3√(2) units.
d² = (3√(2))²+4²-2*3√(2)*4cos45
d = √(10) units.
d = 3.1622776602 units.
d is the radius...
Calculating area x.
Let the square side length be 2a.
b² = a²+(2a)²
b = √(5a²)
b = √(5)a units.
c² = 2a²
c = √(2)a units.
c is the side length of the inscribed regular triangle (equila...
Calculating angle x.
Let the base of the ascribed triangle be 1 unit.
a = 180-20-10-10-100
a = 180-140
a = 40°
(1/sin(100+10)) = (b/sin40)
b = 0.6840402867 units.
c = 180-100-20
c =...
Let the radius of the red circle be r.
Calculating r.
It will be;
√(13²-5²)=√((9+r)²-(9-r)²)+√((4+r)²-(4-r)²)
12=√(36r)+√(16r)
12=10√(r)
√(r)=1.2
r=1.44 unit.
Calculating angle PQR...
