sin75 = a/30
a = 28.9777747887 units.
cos75 = b/30
b = 7.7645713531 units
cos75 = c/15
c = 3.8822856765 units.
d = 15-c
d = 11.1177143235 units.
Area Orange is;
Area rectangle w...
15² = a²+6²
a² = 225-36
a = √(189)
a = 3√(21) units.
b = 2a
b = 6√(21) units.
sin75 = c/b
c = 6√(21)sin74
c = 26.5585692881 units
d = 10+c
d = 36.5585692881 units.
cos75 = e/(6√(...
Shaded Area is;
Area circle with diameter 30 cm - 7(area circle with diameter 10 cm)
= π(½(30))² - 7π(½(10))²
= π(15)² - 7π(5)²
= 225π - 175π
= 50π cm²
Sir Mike Ambrose is the author of the question.
Let CD = 2 units.
Therefore;
Calculating AB.
AB = 1 + (2sin18*tan72 + 2sin36)tan54
AB = 1 + 3.07768353717tan54
AB = 1 + 4.23606797749
AB = 5.236067...
x² = (r+1)² - (r-1)²
Therefore x = 2√(r) unit.
y² = (r+1)² - (2√(r))²
Therefore y = √(r²-2r+1)
y = √(r-1)²
y = (r-1) unit.
z = (r+1) - y
z = (r+1) - (r-1)
Therefore z = 2 units.
a = r+r
Therefore...
a = 2atan(2)°
b = ½(180-a)
b = ½(180-2atan(2))°
tan(½(180-2atan(2))) = c/(0.5x)
0.5 = c/(0.5x)
c = 0.25x cm.
d = x-0.25x
d = 0.75x cm.
Calculating x.
0.5*x*0.75x = 24
x² = 24/(0.75*0.5)
x² = 64...
Let AB = a
Notice.
AB = CD
a² = 2²+1²+2*2*1cosx
a² = 5+4cosx --- (1).
a² = 3²+4²-2*3*4cosx
a² = 25-24cosx --- (2).
Calculating x.
Equating (1) and (2).
5+4cosx = 25-24cosx
28cosx = 20
cosx = (2...
Diameter of the inscribed circle is;
½(AB)
= ½(8)
= 4 units.
a = ½(4)
a = 2 units.
a is the radius of the inscribed circle.
Calculating red length.
Notice, the red length is the side of the inscr...
Let the side length of the regular hexagon be 1 unit.
a = ½(180-108)
108° = single interior angle of the regular pentagon.
180° = sum of angles on a straight line.
a = ½(72)
a = 36°
tan36 = b/0.5...
Let the side length of the regular pentagon be 1 unit.
a² = 1²+1²
a = √(2) units.
b = ½(a)
b = ½√(2) units.
c = ½(360-108-108)
c = ½(360-216)
c = ½(144)
c = 72°
d = 180-108-45
d = 72-45
d = 27°...
