Calculating r.a² = 2(2r)²a = √(2(2r)²)a = 2√(2)r unitsa is the diagonal of the inscribed square.b² = 2r²b = √(2)r units.c = a+b+rc = 2√(2)r+√(2)r+rc = (1+3√(2))r units.c is the diagonal of the ascrib...
Calculating area triangle BAC.a² = √(7)²+3²a = √(16)a = 4 units.b = a+√(7)b = (4+√(7)) units.b is AB.√(7) ~ 34 ~ cCross Multiply.√(7)c = 12c = ⅐(12√(7)) units.d = 3+cd = 3+⅐(12√(7))d = ⅐(21+12√(7)) u...
Calculating x, length DP.sina = 8/10a = asin(4/5)°a is angle BCP.b = 360-90-90-ab = (180-asin(4/5))°b = 126.869897646°b is angle ABC.c = ½(b)c = ½(126.869897646)c = 63.4349488229°c is theta, angle AB...
Calculating Area Yellow.a = 2+20a = 22 units.b²+x² = 20²b = √(400-x²) units.cosy = b/20cosy = √(400-x²)/20 --- (1).10² = 22²+√(400-x²)²-2*22√(400-x²) cosy100 = 484+400-x²-44√(400-x²)cosy44√(400-x²)co...
Calculating ratio AM/BC.Let alpha be x.Let BC be 2 units.It implies;BM = CM = 1 unit.tan(2x) = a/1a = tan(2x)a = (2tanx)/(1-tan²x) --- (1).a is AB.tanx = 2/a --- (2).Therefore, equating (2) in (1).a...
Calculating length x.½*5*a = S5a = 2Sa = ⅕(2S) units.a is CE.x ~ 5b ~ aTherefore;x ~ 5b ~ ⅕(2S)Cross Multiply.⅕(2S)x = 5b2Sx = 25bb = (2Sx)/25 units.b is BC.Calculating x, length AB.½*x*b = 3S+S½*x*(...
Calculating length x.a = 2+3 = 1+4a = 5 units.a is the radius of the ascribed quarter circle.b = a+3b = 5+3b = 8 units.It implies;c*c = 2*bc² = 2*8c = √(16)c = 4 units.d = c-1d = 4-1d = 3 units.There...
Calculating x/y.tana = 4/3a = atan(4/3)°b = 180-ab = (180-atan(4/3))°b = 126.869897646°c² = 3²+1²-2*3*1cos126.869897646c = 3.68781778292 units.(1/sind) = (3.68781778292/sin(126.869897646))d = 12.5288...
Calculating the required angle.Let it be x.Let the square side length be 2 units.a = ½(2)a = 1 unit.tanb = 2/1b = atan(2)°c = 180-bc = (180-atan(2))°(2/sin(180-atan(2))) = (1/sind)d = 26.5650511771°e...
Calculating Area ADPB.Notice.BD = 3 units.CD = 1 unit.a = ½(3)a = 1.5 units.a is AC.b = a+1b = 1.5+1b = 2.5 units.b is OB, the radius of the circle.cosc = a/bc = acos(1.5/2.5)c = 53.1301023542°c is a...
