tana = 5/8
a = atan(5/8)°
b = atan(8/5)°
c = 180-45-a
c = (135-atan(5/8))°
d = (135-atan(8/5))°
(e/sin(atan(8/5))) = (3/sin(135-atan(8/5)))
e = 2.6108558075 units.
(f/sin(atan(5/8...
a² = 24²+7²
a = 25 units.
a is DF.
b²+20² = a²
b² = 25²-20²
b = 15 units.
b is EF.
tanc = 7/24
c = atan(7/24)°
c is angle CED.
tand = 15/20
d = atan(3/4)°
d is EDF.
e = 180-c-d...
√(x-2)-√(x+3) = 1
x-2=(1+√(x+3))²
x-2=1+2√(x+3)+x+3
-6=2√(x+3)
-3=√(x+3)
9=x+3
x=6.
Checking accuracy.
√(6-2)-√(6+3)=?
√(4)-√(9)=?
±2-±3=?
±2+3=?
+2+3≠1
Therefore;
-2+3=1
Let the single side length of the ascribed square be 2 unit.
Therefore area of the ascribed square is;
4 square unit.
Calculating shaded area (area yellow).
It will be;
Area square of single sid...
Calculating Area Red/Area Yellow.
Let R, radius of the equal circles be 1 unit.
Area Yellow is;
2(2(area sector with radius 1 unit and angle 60°) - area regular triangle with side length 1...
Notice!
AC = 7+7
AC = 14 units.
It implies;
14² = 2a²
a² = ½(196)
a = √(98)
a = 7√(2) units.
a is the side length of square ABCD.
Therefore, shaded area yellow is;
Area square w...
sin30 = 10/a
a = 20 units.
a is the side length of the square.
sin30 = b/10
b = 5 units.
Therefore;
Area Yellow is;
Area triangle with height 20 units and base 5 units.
= ½*20*5...
a² = 3²+5²-2*3*5cos60
a = √(19) units.
a = 4.3588989435 units.
a is AC.
b² = 2²+1²-2*2*1cos60
b = √(3) units.
b = 1.7320508076 units.
b is CD.
(√(19)/sin120) = (√(3)/sinc)
c = 20.12830...
Calculating x.
(a+30)*x = (30+15)(30+15)
x = 45²/(a+30) --- (1).
a*x = 15*15
a = 225/x --- (2).
Therefore, Substituting (2) in (1) to get x.
x = 45²/((225/x)+30)
x = 2025÷(225+30x)/x...
5² = 2a²
a² = ½(25)
a = √(½(25)) cm.
a = √(12.5) cm.
b = 5-a
b = (5-√(½(25))) cm.
b = (5-√(12.5)) cm.
It implies, blue area is;
½(b²)
= ½(5-√(½(25)))²
= ½(5-√(12.5))²
= ½(25-10√(12...
