Sin x = a , tan 2x adalah

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Sekolah Menengah AtasMatematika 5+3 poin

A+b=10 sudut A=60 ,sudut B=45.Berapakah sisi-sisi segitiga tersebut ?
Tanyakan detil pertanyaan Ikuti tidak puas? sampaikan! dari Rianwidiarjun 16.11.2014

Jawabanmu

Takamori37
Takamori37 Tutor

a+b = 10
b = 10-a
C = 180-105 = 75 djt
Aturan sin:
displaystyle frac{a}{sin A}=frac{b}{sin B} \ \ frac{a}{sin 60}=frac{10-a}{sin 45} \ frac{a}{frac{1}{2}sqrt{3}}=frac{10-a}{frac{1}{2}sqrt{2}} \ \ frac{a}{sqrt{3}}=frac{10-a}{sqrt{2}} \ \ sqrt{2}a=sqrt{3}(10-a) \ sqrt{2}a=10sqrt{3}-sqrt{3}a \ a(sqrt{3}+sqrt{2})=10sqrt{3} \ a=frac{10sqrt{3}}{sqrt{3}+sqrt{2}}=frac{10sqrt{3}}{sqrt{3}+sqrt{2}}timesfrac{sqrt{3}-sqrt{2}}{sqrt{3}-sqrt{2}} \ \ a=frac{30-10sqrt{6}}{3-2} \ \ a=30-10sqrt{6}
b=10-a \ b=10-(30-10sqrt{6}) \ b=10sqrt{6}-20 \ \ displaystyle frac{b}{sin B}=frac{c}{sin C} \ \ frac{10sqrt{6}-20}{frac{1}{2}sqrt{2}}=frac{c}{frac{1}{4}(sqrt{6}+sqrt{2})} \ 10sqrt{6}-20=frac{c}{frac{1}{2}(sqrt{3}+1)} \ c=frac{1}{2}(sqrt{3}+1)(10sqrt{6}-20) \ c=(sqrt{3}+1)(5sqrt{6}-10) \ c=5sqrt{18}-10sqrt{3}+5sqrt{6}-10 \ c=5sqrt{6}-10sqrt{3}+15sqrt{2}-10