F.4 Maths
2010-03-13 7:14 pm
Consider △ABC,where sinA:sinB:sinC=2:3:4 and A=29°.If the perimeter of △ABC is 108cm,solve △ABC.
回答 (1)
2010-03-13 10:22 pm
✔ 最佳答案
Let 3 sides of △ABC be a , b , c :By sine formula :
a : b : c = sinA:sinB:sinC = 2:3:4
The perimeter of △ABC is 108cm , so
a + b + c = 108
So a = 108 * 2/(2+3+4) = 24cm
b = 24 * 3/2 = 36cm
c = 24 * 4/2 = 48cm ;
sinA : sinB = a : b
sin 29 : sinB = 24 : 36
sinB = (sin29) * 36/24
B = 46.653375°
C = 180 - 29 - 46.6553375 = 104.3466°
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