Matematica esercizio 181,182,184

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

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 

teorema dei seni :

sin 60° / 30 = sin A/20

sin A = 10√3/30 = √3/3 

angolo A = arcsin (√3/3) = 35,26 m

angolo B = 180-(60+35,26) = 84,74°

sin B = 0,9958

AA' = 30*0,9958*2/√3 = 34,5 m 

20/sin 100 = 12/sin c

sin c = 3sin 100/5 = 0,591 

c = arcsin 0,591 = 36,22°

angolo C = 180-(60+45) = 75°

12*2/√2 = AB*4/(√2+√6)

AB = 24(√2+√6)/4√2 = 6(1+√3)

angolo A = 180-(88+22) = 70°

15/sin 22 = AC/sin 88

AC = 15*sin 88/sin 22 = 15*0,9994/0,3746 = 40,0

angolo B = 180-(50+75) = 55°

15/sin 75 = AC/sin 55

AC = 15*sin 55/sin 75 = 15*0,8192/ 0,9659 = 12,72 

angolo A = 180-(75+20) = 85°

40/sin 75 = AC/sin 20°

AC = 40*sin 20/sin 75 = 40*0,3420/0,9659 = 14,16

angolo C = 180-(60+20) = 100°

20/sin 20 = AB/sin 100

AB = 20*sin 100/sin 20 = 20*0,9848/0,3420 = 57,59

angolo B= arccos(-3/4) = 138,6°

angolo C = arcsin (2/5) = 

10√7/sin 138,6 = 5AB/2

2√7/sin 138,6 = AB/2

AB = 4√7/sin 138,6 = 16,00