a² = 3²+4²
a = √(25)
a = 5 units.
2b² = 5²
b² = (25/2)
b = √(25/2)
b = ½(5√(2)) units.
b is the radius of the semi circle.
c = 90+45
c = 135°
(½(5√(2))/sin135) = (3/sind)
d = 36.8698976462°
e =...
r = ½(7) units.
r is the base radius of the cylinder.
H = 6 units.
H is height.
h = 10-6
h = 4 units.
h is height.
Therefore, volume of the cylinder is;
πr²H+½(πr²h)
= π*(7/2)²*6+½*π...
Calculating R, radius of the circle.
b = 360-240
b = 120°
b is the angle that is subtended by the 9 units chord with the radius of the circle.
R, radius of the circle is;
Observing Cosine Rule.
9...
Let the side length of the regular octagon be 1 unit.
Notice!
x, radius of the green inscribed circle is 1 unit.
a = ⅛*180(8-2)
a = ⅛(1080)
a = 135°
a is the single interior angle of the regular o...
a = 10 units.
a is the radius of the circle.
b = (20-2x) units.
c = ½(b)
c = ½(20-2x)
c = (10-x) units.
It implies;
Calculating x.
10² = 2c²
100 = 2(10-x)²
100 = 200-40x+2x²
2x²-...
Let the square side length be a.
b² = 2a²
b = √(2)a units.
b is AC = BD, the diagonal of the square, ABCD.
c = x units.
d = (3-x) units.
Calculating x, observing similar plane shape (right-angle...
Notice!
The composite figure (plane shape) is not drawn to scale.
Let the side length of triangle ABC (equilateral triangle) be 1 unit.
1² = 2a²-2a²cos120
1 = 3a²
a = √(1/3)
a = ⅓√(3) units.
a is...
Let the radius of the inscribed circle be x.
a = (3-x) units.
b = 7-3
b = 4 units.
c = (7-x) units.
d = a+c
d = (3-x)+(7-x)
d = (10-2x) units.
Therefore, x (radius of the inscribe...
Notice!
The gray inscribed triangle is equilateral.
Calculating length x.
4² = 2a²-2a²cos120
16 = 3a²
a = √(16/3)
a = ⅓(4√(3)) units.
a = 2.3094010768 units.
a is the radius of the circle.
b² = 2...
Calculating length x.
5² = 8²+7²-2*8*7cosa
112cosa = 64+49-25
cosa = 88/112
a = acos(88/112)
a = 38.2132107017°
a is the angle opposite 5 units.
(5/sin38.2132107017) = (7/sinb)
b = 60°
b is the an...
