7² = 3²+5²-2*3*5cosa
30cosa = 34-49
cosa = (-15)/30
a = acos(-½)
a = 120°
b = 2a
b = 240°
c = 360-b
c = 120°
tan60 = 3.5/d
d = 3.5/√(3)
d = ⅓(3.5√(3))
d = ⅙(7√(3)) units.
There...
Notice!
Radius, a of the inscribed circle is 4 units.
Radius, b of the inscribed semi circle is 7 units.
3²+4² = c²
c = √(25)
c = 5 units.
d² = 5²+4²
d = √(41) units.
tane = 3/4
e...
Shaded area will be;
Area semi circle of radius √(2) cm - area quarter circle of radius 2 cm + area square of single side length √(2) cm.
= ½(√(2))²π - ¼(2²)π + (√(2))²
= π-π+2
= 2 cm²
Shaded area will be;
Area quarter circle of radius 2 unit + 2(area quarter circle of radius √(2) unit - area triangle of height and base √(2) unit respectively).
= ¼(4π) + 2(¼(2π) - ½(2))
= π...
Let the inscribed square side be a.
b² = 2a²
b = √(2)a cm.
b is the diagonal of the inscribed square.
c = 90+45
c = 135°
It implies, calculating a, the inscribed square side length.
1...
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...
