Let the required length be x.
Therefore, analysing the composite plane shape.
It implies, the required length, x will make a right-angled isosceles triangle with two radii length, 4 units eac...
Notice!
The composite plane shape consist of two congruent quarter circles with radius 2 units each.
a = 3-2
a = 1 unit.
cosb = 1/2
b = acos(½)°
b = 60°
Area green is;
2(area sector...
Calculating angle x.
Notice!
The inscribed triangle is isosceles.
Let the base be 1 unit.
It implies;
a = 180-80-40
a = 60°
(b/sin80) = (1/sin60)
b = 1.1371580426 units.
(1/sin...
Blue area is;
Area sector with radius 3√(2) unit and angle 30° - area isosceles triangle with two equal length 3√(2) unit and angle 30°.
= (30πx(3√(2))²÷360) - (0.5x(3√(2))²sin30)
= (18π)/12...
a² = 5²+2.5²-2*5*2.5cos120
120° is the single interior angle of the regular hexagon.
it implies;
a = 6.6143782777 units.
(6.6143782777/sin120) = (2.5/sinb)
b = 19.1066053509°
c = 120-b
c...
Calculating x.
a²+(x-3)² = 10²
a² = 100-x²+6x-9
a² = 91+6x-x²
a = √(91+6x-x²) cm.
It implies;
(a+x)² = (x-3)²+(x+4)²
(√(91+6x-x²)+x)² = x²-6x+9+x²+8x+16
91+6x-x²+2x√(91+6x-x²)+x² = 2x²+2x+25
2x√(...
Calculating Length MN.
Let BD = a.
b = 180-30-75
b = 75°
b is angle BDC.
Notice!
Area ABCD = 10 square units.
Calculating a.
It implies
0.5*3*a*sin60 + 0.5*a²sin30 = 10
¼(3√(...
Notice!
The composite plane shape consist of two half circles with equal diameter, 10 units each.
Radius = 5 units each.
Calculating shaded area.
a = 180-2*30
a = 120°
Shaded Area i...
Let the single side length of the equilateral triangle be 4 unit.
Therefore;
Shaded area ÷ Area circle exactly in decimal is;
(Area sector with radius √(3) unit and angle (180-2(sin–¹(sin60...
sin15 = a/6
a = 1.5529142706 units.
a is CD.
cos15 = b/6
b = 5.7955549577 units.
b is BD.
c² = 4²+6²-2*4*6cos30
c = 3.2296719057 units.
c is AC.
(3.2296719057/sin30) = (4/sind)
d =...
