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dasha17110
@dasha17110
June 2022
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в треугольнике авс проведена медиана вм и известно что синус авм/синус свм =1/2. найти отношение вс/ав
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nafanya2014
Verified answer
S(Δ ABM)=AM·h/2
S(ΔBMC)=MC·h/2
AM=MC
Значит
S(Δ ABM)=S(ΔBMC)
S(Δ ABM)=AB·BM·sin∠ABM
S(ΔBMC)=BM·BC·sin ∠CBM
AB·BM·sin∠ABM=BM·BC·sin∠CBM
разделим на ВМ
AB·sin∠ABM=BC·sin∠CBM
BC:AB=sin∠ABM:sin ∠CBM=1:2
Ответ. ВС:АВ=1:2
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Answers & Comments
Verified answer
S(Δ ABM)=AM·h/2S(ΔBMC)=MC·h/2
AM=MC
Значит
S(Δ ABM)=S(ΔBMC)
S(Δ ABM)=AB·BM·sin∠ABM
S(ΔBMC)=BM·BC·sin ∠CBM
AB·BM·sin∠ABM=BM·BC·sin∠CBM
разделим на ВМ
AB·sin∠ABM=BC·sin∠CBM
BC:AB=sin∠ABM:sin ∠CBM=1:2
Ответ. ВС:АВ=1:2