Let CM be x.
Calculating x.
x+1 - x+3
1 - 2
Cross multiply.
2x+2=x+3
x = 1 units.
Therefore,
CM = 1 units.
Therefore angle C is;
Sin C = ½
C = 30°
Calculating AB.
N...
Sir Mike Ambrose is the author of the question.
Notice;
Side length of the congruent regular hexagon is 2 units.
(a) Calculating
Length Blue ÷ Length Red.
Length Blue is;
Let it be x....
Shaded red area is;
Area quarter of radius 10 units - Area sector of radius 10 units and angle 30° - Area equilateral triangle of single side length 5 units - Area sector of radius 5 units and a...
Radius of the circle is;
5-(√(18-18cos(180-2atan(4/3)))
= 5-3.6
= 1.4 units
= (7/5) units.
Therefore area of the circle is;
π(7/5)²
= (49/25)π square units.
Red shaded area will be;
Area square with single side length 3 inches
= 3 * 3
= 9 square inches.
Sir Mike Ambrose is the author of the question.
Calculating Area Orange.
Radius of the circle, r is;
(5-r)²=18-18cos(180-2atan(4/3))
(5-r)²=12.96
5-r=√(12.96)
5-r=3.6
Therefore;
r =...
Let BD = x
Calculating x;
5²= √(9+x²)²+√(9+(x+5)²)²-2√(9+x²)*√(9+(x+5)²)cos45
It implies;
x = 1 unit.
Calculating AC.
AC = √(9+(x+5)²)
And x = 1
It implies;
AC = √(9+(1+5)²...
Let the radius of the quarter circle be 2 units.
Radius, r of the small inscribed semi circle is;
(2+r)²=1+(2-r)²
r = ⅔ units.
Calculating angle x;
½(atan(3/4))
= 18.43494882292°
Let Alpha be x.
Calculating x;
½(180-atan2)-atan(0.5)
x = ½(90-atan(0.5))
It implies;
tan x exactly is;
= tan(½(90-atan(0.5)))
Calculating Area Orange.
Notice, Area Orange is...
a = ½(360-90)
a = ½(270)
a = 135°
It implies;
b² = 1²+√(2)²-2√(2)cos135
b = √(5) units.
Calculating c, radius of the quarter circle.
2c² = b²
2c² = √(5)²
c = √(5/2) units.
Again,...
