73
punti
Livello 1
182
angolo LNM = arccos 2√2 /3 = 19,4712°
sen LNM = sen 19,4712° = 1/3
angolo NML = 180-(30+19,4712) = 130,5288°
seno 130,5288° = 0,760
60/ (1/3) = MN/0,5
MN = 30/(1/3) = 90 cm
60/ (1/3) = LN/0,760
LN = 180*0,760 = 136,814
check = 30*(2*2^0,5+3^0,5) = 136,814
117316
punti
Genius III
181
DAB = 60°
ABD = 45°
ADB = 75°
12/sen 60° = AD/sen 45°
AD = 12*√2 /2 /( √3 /2) = 12√2 / √3
sen 75 = sen(30+45) = 0,5*√2 /2 + √3 /2*√2 /2 = √2(1+√3)/4
12/sen 60° = AB/sen 75°
AB = 12(√2(1+√3)/4)*2/√3 = 3(√2(1+√3) / √3
perimetro = 2(AD+AB) = 2(12√2+3(√2(1+√3))) / √3
117316
punti
Genius III