Question

Calcule o perímetro do triângulo ABC sabendo que A=45°, B=60° e a=5cm

Answer 1

45 + 60 + c = 180
105 + c = 180
c = 180 - 105
c = 75

a/sen A = b/sen B = c/sen C
5/sen 45 = b/sen 60
5/ \/2/2 = b/ \/3/2
b\/2/2 = 5\/3/2
b\/2 = 5\/3
b = 5\/3 / \/2
b = 5\/3\/2 / 2
b = 5\/6/3

sen 75 = sen (30+45) = sen 30.cos 45 + sen 45. cos 30
= 1/2.\/2/2 + \/2/2.\/3/2
= \/2/4 + \/6/4
= (\/2+\/6)/4

P = 5 + 5\/6/3 + (\/2+\/6)/4
mmc (4 e 6) = 12
P = (12:1.5)/12 + (12:3.5\/6)/12 + (12:4.(\/2+\/6)/12
P = [60 + 20\/6 + 3(\/2.\/6)] / 12