Calculating 2R.R is the radius of the inscribed circle.a = (8-R) units.b = (8+R) units.b¹ = (16-R) units.c²+R² = (16-R)²c² = 256-32R+R²-R²c = √(256-32R) units.R is;√(256-32R)²+(8-R)² = (8+R)²256-32R+...
Calculating the radius, R and circumference of the circle.a² = 4²+8²-2*4*8cos60a = 6.92820323028 units.a is BD.(6.92820323028/sin60) = (8/sinb)b = 90°b is angle BDC.c² = 7²+4²-2*4*7cos120c = 9.643650...
Calculating Square Area.Let x be the side length of the square.a = 4+2a = 6 cm.b²+x² = 6²b² = 36-x²b = √(36-x²) units.c = ½(4)c = 2 units.Calculating x² (Area of the square).6 ~ x√(36-x²) ~ 2Cross Mu...
Calculating x (length AD).a = 180-60a = 120°a is angle ABC.cos60 = 7/bb = 14 units.tan60 = c/7c = 7√(3) units.d = b+9d = 14+9d = 23 units.sin60 = 23/e½√(3) = 23/ee = 46/√(3)e = ⅓(46√(3)) units.Theref...
Calculating x.Notice.The ascribed plane shape is a square.tana 10/5a = atan(2)°b = 180-ab = (180-atan(2))°c = ½(b)c = (90-0.5atan(2))°d = (5-y) units.y is the radius of the inscribed circle.Calculati...
Calculating x.tan30 = a/8√(3)a = 8a = ⅓(8√(3)) units.sin30 = a/b½ = ⅓(8√(3))/bb = ⅓(16√(3)) units.c = 8+6+xc = (14+x) units.It implies, x is;⅓(8√(3)) ~ x⅓(16√(3)) ~ (14+x)Therefore;½ = x/(14+x)Cross...
Calculating x.a = (x+4) units.a is the radius of the quarter circle.b² = 4²+2²b = √(20)b = 2√(5) unit.tanc = 2/4c = atan(0.5)°d = 90+cd = (90+atan(0.5))°Therefore, x is;(x+4)² = x²+(2√(5))²-2x*2√(5)c...
Calculating Yellow Area BCT.Notice.AB = 2 cm.BC = 6 cm.Let x be the radius of the circle.a = x-ABa = (x-2) cm.b²+(x-2)² = x²b² = x²-(x²-4x+4)b² = 4x-4b = √(4x-4) cm.c = ½(BC)c = ½(6)c = 3 cm.Calculat...
Calculating R, radius of the half circle.a = (R-8) units.b = R+ab = R+(R-8)b = (2R-8) units.c = ½(b)c = ½(2R-8)c = (R-4) units.d = 2R units.Therefore, R is;(R-4) ~ 8√(3)8√(3) ~ 2RCross Multiply.2R(R-...
Calculating R, radius of the circle.sina = 10/(5√(5))a = asin(2/√(5))°b = 90-ab = (90-asin(2/√(5)))°Calculating R.cosb = ½(5√(5))/Rcos(90-asin(2/√(5))) = ½(5√(5))/R2Rcos(90-asin(2/√(5))) = 5√(5)R = 5...
