в треугольнике abc угол c равен 90° BC=4, sinB=3/√10 Найдите АС. Created by Ninel07. geometriya-ru

√10 Найдите АС...

Ninel07 @Ninel07

August 2022 1 14 Report

в треугольнике abc угол c равен 90° BC=4, sinB=3/√10 Найдите АС

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Dимасuk

Verified answer

CosB = √1 - sin²B = √1 - 9/10 = 1/√10 = √10/10
cosB = BC/AB <=> AB = BC/cosB
AB = 4/1√10 = 4√10.
Найдём АС по теореме Пифагора:
AC = √16•10 - 16 = √16•9 = 4•3 = 12.
Ответ: АС = 12.

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