Sir Mike Ambrose is the author of the question.
sin30 = (4√(3))/a
a = 8√(3) units.
a is AC.
AB = ⅓(a)
AB = ⅓(8√(3)) units.
cos30 = b/⅓(8√(3))
b = ⅓(8√(3))*½√(3)
b = 4 units.
sin30 =...
Calculating angle x, observing sine rule.
(80/sin(2x)) = (50/sinx)
80sinx = 50sin(2x)
8sinx = 10sinxcosx
4 = 5cosx
x = acos(4/5)
x = 36.8698976458°
Therefore;
Angle 2x is;
2*36.869...
Observing similar plane shape (right-angled) side length ratios.
(6+x) - (6+2+6)
6 - 8
Cross Multiply.
8(6+x) = 6(14)
48+8x = 84
8x = 84-48
8x = 36
x = ½(9) units.
Again;
Observi...
Calculating R, radius of the small inscribed quarter circle.
a = 2*18
a = 36 units.
a is the radius of the ascribed quarter circle.
b = (18+R) units.
It implies;
R, radius of the small...
sin60 = 18/a
a = 20.7846096908 units.
tan60 = 18/b
b = 10.3923048454 units.
c+270+60+30+135 = 180(5-2)
c = 540-495
c = 45°
d² = 2(18²)
d = 18√(2) units.
d = 25.4558441227 units.
e...
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...
