Calculating x.Notice.The angle formed at the meet point (vertex) of length 4 units and x units is equal the angle formed at the meet point (vertex) 9 units and x units.It implies, two similar plane s...
Calculating Shaded Fraction.Let the bigger inscribed semi circle radius be 2 units.Let the big inscribed semi circle radius be r.Let the inscribed circle radius be q.Calculating r.(2+r)² = 2²+(4-r)²4...
Calculating Length EF.Let FC = x.Let CE = y.Therefore;5+x = y+4x = y-1 --- (1).Notice;Triangle AEF is similar to triangleEFC.It implies;5+x ~ y 4 ~ xCross Multiply.x²+5x = 4y --- (2).Substituting...
Calculating Theta.Let it be x Let 1 units be the side length of the square.tan15 = b/1b = tan15 units.b = 0.26794919243 units.b is length AF.a+b = 1a = 1-ba = 1-0.26794919243a = 0.73205080757 units.a...
Calculating x/y please.Notice.The side length of the regular decagon and regular pentagon are equal.Let 2 units be the side length of the regular decagon.Calculating x.a = ⅒*180(10-2)a = 144°a is the...
Calculating R, radius of the circle.a = (R-6) units.b = (6+R) units.It implies;b*a = 3*7(6+R)(R-6) = 216R-36+R²-6R = 21R²-36 = 21R² = 21+36R² = 57R = √(57) units.R = 7.54983443527 units.
Notice.R-r = 10 cm.It implies;R = (10+r) cm.R is the side length of the ascribed square.Calculating length AB.a = R-ra = 10 cm.b = ½(R) units.It implies;R² = 10²+(½(R))²R²-¼(R²) = 100¼(3R²) = 1003R²...
Calculating Length Red.Notice.Radius of the half circle is 5 units.a = (5-x) units.Calculating x.5² = 3²+(5-x)²16 = 25-10x+x²x²-10x+9 = 0Therefore;x ≠ 9 units.x = 1 unit.Recall.a = 5-xAnd x = 1 unit....
Calculating Length QO.Let R be the bigger inscribed circle radius.Let r be the smaller inscribed circle radius.It implies;R+r = 6√(3)-6 = 4.4 units.R+r = 4.4 -----(1).And the radius of the ascribed s...
Sir Mike Ambrose is the author of the question.Let a be the equal lengths inscribing triangle ABC.Calculating a.½(a)² = 15a = √(30) units.b = 180-60-45b = 75°b is angle BAC.c = 180-2bc = 30°d² = 2√(3...
