a² = 4²+6²-2*4*6cos60
a = 5.2915026221 units.
(5.2915026221/sin60) = (4/sinb)
b = 40.8933946491°
c² = 6²+2²-2*6*2cos60
c = 5.2915026221 units.
(5.2915026221/sin60) = (2/sind)
d = 19.1066053509°...
Let the inscribed blue equilateral triangle side length be 1 unit.
Area Blue is;
0.5*1*1sin60
= ¼√(3) square units.
= 0.4330127019 square units.
0.5² = 2-2cosa
2cosa = 2-0.25
cosa = (1....
Let the radius of the ascribed circle be 1 unit.
Area ascribed circle is;
πr²
= π(1)²
= π square units.
Calculating area inscribed red circle.
Let it's radius be r.
sin30 = a/1
a...
Method A.
15² = (0.5*24)²+a²
a² = 225-144
a = √(81)
a = 9 units.
a is the side length of the two equal lengths each.
tanb = 9/12
b = atan(¾)°
c = 90-b
c = atan(4/3)°
Therefore, r,...
a*x = 15*15
ax = 225
a = 225/x --- (1).
(30+a)*x = (30+15)*(30+15)
ax+30x = 2025 --- (2).
Substituting (1) in (2).
(225/x)x+30x = 2025
225+30x = 2025
30x = 2025-225
30x = 1800
x = 1...
Let R=the bigger inscribed circle radius.
Let r=the smaller inscribed circle radius.
It implies;
R+r=6√(3)-6=4.4
R+r=4.4 -------(1).
And the radius of the ascribed semi circle is 6 un...
a² = 2-2cos120
a = √(3) units.
(2/sin30) = (√(3)/sinb)
b = 25.6589062733°
c = 180-30-b
c = 124.3410937267°
d² = √(3)²+2²-2*2√(3)cos124.3410937267
d = 3.3027756377 units.
e² = 3.3027...
Let a be the side length of the regular hexagon.
Calculating a.
(14/sin60) = (16/sinb)
b = 81.7867892983°
c = 180-60-b
c = 38.2132107017°
It implies;
(a/sin38.2132107017) = (14/sin...
Observing similar plane shape (scalene triangle) side length ratios.
Therefore;
y - 8
20 - 22
It implies;
(y/20) = (8/22)
(y/20) = (4/11)
Cross Multiply.
11y = 80
y = 80/11 units.
y = 7.2...
3² = 2c²-2c²cos108
108° is the single interior angle of the regular pentagon.
It implies;
9 = 2.6180339887c²
c² = 3.4376941013
c = 1.8541019663 units.
c is the side length of the regular pent...
