Length AD is;
AD = 3√(15) cm.
Therefore;
Area Orange exactly in cm² is;
Area triangle with height √(15) cm and base 3√(15) cm + Area triangle with height 5√(6) cm and base ¼√(615)sin(180-atan(3)-a...
Gradient of the curve at x = 3 is;
dy/dx = (-19/20)
It implies;
Area yellow exactly in square unit decimal is;
Area triangle with height (5/(4sin(atan(19/20)))) unit and base (5/(4sin(atan(20/19)...
18² = 14²+16²-2*14*16cosa
448cosa = 14²+16²-18²
a = acos((14²+16²-18²)/448)
a = 73.39845040098°
(18/sin73.39845040098) = (14/sinb)
b = 48.18968510422°
c = 180-48.18968510422-73.39845040098
c = 58....
Let AB be 5 units.
Radius, r of the inscribed circle is;
5*(2/5)
r = 2 units.
a = ⅛(180*6)
a = 135°
2b² = 25
b = ½(5√(2)) units.
c = 180-0.5(135)-45
c = 67.5°
sin22.5 = ½(5√(2))/d
d = 9.2387953...
Let alpha be x.
Therefore;
(12/sin2x)=(8/sinx)
And;
Sin2x = 2sinxcosx
Therefore;
(12/2sinxcos)=(8/sinx)
6 = 8cosx
x = acos(6/8)°
2x = 2acos(6/8)°
Let y be the third interior angle.
y = (180-3acos...
Let the side length of the regular hexagon be 1 unit.
a = ⅙(180(6-2))
a = ⅙(180*4)
a = 120°
a is the single interior angle of the regular hexagon.
b² = 1+1-2cos120
b = 2-2cos120
b = √(3) units.
b...
Let the side length of the green regular hexagon be 1 unit.
Therefore the angle theta to 2 d. p. is;
(atan(0.5÷(tan72-sin60)) + atan(0.5÷(tan72+sin60)))°
= (12.7389799507+7.22564879327)°
= 19.9646...
2a+c = 180
c = 180-2a --- (1).
2b+d = 180
d = 180-2b --- (2).
e = 180-112
e = 68°
x+a+b = 180
a+b = 180-x --- (3).
It implies;
c+d+68 = 180
180-2a+180-2b+68 = 180
248-2(a+b) = 0 --- (4).
Theref...
Area green exactly in cm² is;
Area ABCD - Area trapezoid with parallel sides (9-2√(3)) cm and (24√(3)-39) cm, and height 6 cm.
= (54-6√(3)) - ½*6((9-2√(3))+(24√(3)-39))
= (54-6√(3)) - 3(22√(3)-30)...
