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samodurovadasa300606
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August 2022
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zmeura1204
Ответ:
TR=36ед
Решение:
S(∆KSF)=1/2*SF*KF*sin∠SFK.
sin∠SFK=2*S(∆KSF)/(SF*KF)=
=2*42/(20*15)=7/25.
Тождество:
sin²F+cos²F=1
cosF=√(1-7/25)=√(625/625-49/625)=
=√(576/625)=24/25
Теорема косинусов:
SK=√(SF²+KF²-2*SF*KF*cosF)=
=√(20²+15²-2*20*15*24/25)=
=√(400+225-576)=√49=7ед.
∆КSF~∆KTR, по углам.
КS/KT=SF/TR
7/12,6=20/TR
TR=20*12,6/7=36ед
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Answers & Comments
TR=36ед
Решение:
S(∆KSF)=1/2*SF*KF*sin∠SFK.
sin∠SFK=2*S(∆KSF)/(SF*KF)=
=2*42/(20*15)=7/25.
Тождество:
sin²F+cos²F=1
cosF=√(1-7/25)=√(625/625-49/625)=
=√(576/625)=24/25
Теорема косинусов:
SK=√(SF²+KF²-2*SF*KF*cosF)=
=√(20²+15²-2*20*15*24/25)=
=√(400+225-576)=√49=7ед.
∆КSF~∆KTR, по углам.
КS/KT=SF/TR
7/12,6=20/TR
TR=20*12,6/7=36ед