Calculating Alpha.Let it be x.Let a be the radius of the ascribed quarter circle.b = (a-√(2)) units.c = (a-2√(2)) units.Calculating a.a ~ (a-√(2))(a-2√(2)) ~ √(2) Cross Multiply.√(2)a = a²-2√(2)a-√(2...
Calculating r, radius of the inscribed circle.Notice.Angle ABD = ¼(60)Angle ABD = 15°tan30 = r/a1/√(3) = r/aa = √(3)r units.b = 2ab = 2√(3)r units.b is the side length of the ascribed regular triangl...
Calculating the green area x.Notice.5 units is the height of the green triangle and 15 units is the base.It implies, area green (x) is;½*5*15= ½(75)= 37.5 square units.
Calculating theta.Let it be x.Let angle BAD be a.b+a+30 = 180b = (150-a)°b is angle ADB.It implies;x+b = 180x+150-a = 180x = (30+a)°Again, a is theta.c = 180-100c = 80°c is the supplementary angle of...
Calculating Angle x.a = 90-40a = 50°a is angle EOQ.b = ½(180-a)b = ½(180-50)b = ½(130)b = 65°Therefore the required angle, x is;x = ½(90)+bx = 45+65x = 110°
Calculating x.a = ½(180-60)a = ½(120)a = 60°a is angle DCO = angle COD = angle CDO, making triangle CDO equilateral. b = a-45b = 60-45b = 15°b is angle ECO = angle CEO.c = 180-2bc = 180-2(15)c = 150°...
Calculating Area Blue.a = 8-2a = 6 units.cosb = 6/8b = acos(3/4)°Therefore, blue area is;½*8*8sin(acos(3/4))=½*8*8*0.66143782777= 32*0.66143782777= 21.1660104886 square units.
Calculating x.a = (2+x) units. Is the radius of the half circle.b = 2+ab = 2+2+xb = (4+x) units.Therefore, length x is;a²+a² = b²(2+x)²+(2+x)² = (4+x)²2(4+4x+x²) = 16+8x+x²8+8x+2x² = 16+8x+x²8+2x² =...
Calculating Shaded Area.Notice.ABCD is a square.Let x be the side length of the square.a²+x² = 40²a = √(1600-x²) units.a is BF.b = x-ab = (x-√(1600-x²)) units.b is AF.It implies;cosc = x/40 --- (1).c...
Calculating L, length of the ascribed regular pentagon.a = (x+8) units.b = ⅕(180(5-2))b = ⅕*180*3b = 108°b is the single interior angle of the regular pentagon.c = 180-bc = 180-108c = 72°Calculating...
