Предмет: Геометрия, автор: Аноним

У трикутнику АВС ВС= 2 см. Точка D лежить на АС, причому АD= 3cм, DC= 1cм, BD= 1,5 см. Знайти АВ.​

Ответы

Автор ответа: danyazeml31
1

Ответ:AB=3 cm

Объяснение:

В треугольнике АВС ВС=2см.

Точка D принадлежит АС, причем АD=3 см, DС=1 см, ВD=1,5 см.

Найдите длину отрезка АВ.  

АВ можно найти по т. косинусов.

Найдем косинус угла С  

Рассмотрим треугольник DВС.

В нем даны длины всех сторон.  

ВD²=ВС²+DС² - 2* ВС*DС*сos∠DCВ  

2,25=4+1 - 4*сos ∠DCВ  

-2,75= - 4 сos ∠DCВ

сos ∠DCВ= -2,75:(- 4)=0,6875  

АВ²=АС²+ВС² -2*АС*ВС*сos ∠DCВ  

АВ²=16+4 -16*0,6875  

АВ²=20-11=9  

АВ=3 см  

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