Calculating GH/HI.Let 2 units be the side length of the regular pentagon.Therefore, 1 unit is the radius of the circle.a = ⅕*180(5-2)a = 108°a is the single interior angle of the regular pentagon.b =...
Calculating length MN.let x be the radius of the circle.a = ½(15)a = 7.5 units.b = 24-ab = 24-7.5b = 16.5 units.c²+b² = 24²c = √(24²-16.5²)c = 17.4284250579 units.d²+a² = x²d = √(x²-7.5²) units.e = x...
Calculating r, radius of the yellow inscribed circle.Notice.OB = 16, radius of the ascribed quarter circle.OM = AM.It implies;OM = AM = ½(16)OM = AM = 8 units.OM = AM = diameter of the inscribed red...
Calculating Area Shaded (Area ABC).Let AC be x.a = 4+1a = 5 units.Calculating x.x ~ 54 ~ xCross Multiply.x² = 20x = 2√(5) units.Again, x is AC.sinb = 4/xb = asin(4/(2√(5)))°b = asin(2/√(5))°tanb = c/...
Calculating x.(x+4)² = 4²+(x+2)²Where (x+4) is the radius of the quarter circle.It implies;x²+8x+16 = 16+x²+4x+48x = 4x+44x = 4x = 1 unit.
Calculating R.b = 60°b is the single interior angle of the ascribed regular triangle (equilateral triangle).c = ½(b)c = 30°tan30 = R/d1/√(3) = R/dd = √(3)R cm.e = R+Re = 2R cm.f = 2d+ef = 2√(3)R+2Rf...
Calculating the indicated angle.Let it be x.Let 1 unit be the radius of the congruent circles each.a = ⅕*180(5-2)a = ⅕*180*3a = 108°a is the single interior angle of the inscribed regular pentagon.1²...
Calculating Area Green (equilateral triangle).Let x be the side length of area green.a = 90-60a = 30°a is angle OXY.cos30 = b/x½√(3) = b/xb = ½√(3)x units.b is OX.Calculating x.x²+(½√(3)x)² = √(7)²x²...
Calculating C, circumference of the circle in terms of π.Let r be the radius of the circle.a = (r-6) units.b = (r+6) units.Calculating r.(r-6)(r+6) = 3*7r²-36 = 21r² = 57r = √(57) units.Therefore, ci...
Calculating x, radius of the circle.sina = 4/16a = asin(¼)°a is angle RTS.b = 90-ab = (90-asin(¼))°b = 75.5224878141°b is angle OTS.It implies x, radius of the circle is;cosb = (½*16)/xcos(75.5224878...
