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27 августа 2023 01:45
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В треугольнике ABC AC=BC, sinACD=2/√5, AH и CD высоты. Найдите tgBAH
1
ответ
Для решения данной задачи, нам понадобится использовать теорему синусов и теорему Пифагора.
Из условия задачи, мы знаем, что AC = BC и sin(ACD) = 2/√5.
Так как AC = BC, то треугольник ABC является равнобедренным.
Из теоремы синусов, мы можем записать:
sin(ACD) / CD = sin(CAD) / AC
2/√5 / CD = sin(CAD) / AC
sin(CAD) = (2/√5) * CD / AC
Так как треугольник ABC является равнобедренным, то угол CAD равен углу CBA.
Из теоремы Пифагора, мы можем записать:
AC^2 = AH^2 + CH^2
Так как AC = BC, то CH = BC / 2
AC^2 = AH^2 + (BC / 2)^2
AC^2 = AH^2 + BC^2 / 4
Из условия задачи, мы знаем, что AC = BC, поэтому:
AC^2 = AH^2 + AC^2 / 4
AH^2 = AC^2 - AC^2 / 4
AH^2 = 3AC^2 / 4
AH = √(3AC^2 / 4)
Теперь мы можем найти sin(CAD):
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / BC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD
Из условия задачи, мы знаем, что AC = BC и sin(ACD) = 2/√5.
Так как AC = BC, то треугольник ABC является равнобедренным.
Из теоремы синусов, мы можем записать:
sin(ACD) / CD = sin(CAD) / AC
2/√5 / CD = sin(CAD) / AC
sin(CAD) = (2/√5) * CD / AC
Так как треугольник ABC является равнобедренным, то угол CAD равен углу CBA.
Из теоремы Пифагора, мы можем записать:
AC^2 = AH^2 + CH^2
Так как AC = BC, то CH = BC / 2
AC^2 = AH^2 + (BC / 2)^2
AC^2 = AH^2 + BC^2 / 4
Из условия задачи, мы знаем, что AC = BC, поэтому:
AC^2 = AH^2 + AC^2 / 4
AH^2 = AC^2 - AC^2 / 4
AH^2 = 3AC^2 / 4
AH = √(3AC^2 / 4)
Теперь мы можем найти sin(CAD):
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / BC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD / AC
sin(CAD) = (2/√5) * CD
0
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27 августа 2023 01:46
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