Задание 4, стр 60

Question

Дан треугольник ABC со сторонами AB = 18, BC = 12, AC = 18. Через сторону AC проведена плоскость $\alpha$, которая составляет угол 45º с плоскостью треугольника. Найдите расстояние от точки В до плоскости $\alpha$.

Gimli · Accepted Answer

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\end{figure}

Находим ВМ по теореме Пифагора:
$$18^2-(18-x)^2=12^{2}-x^{2}$$
$$x(36-x)=144-x^{2}$$
$$36x=144\implies x=4$$
Значит, высота ВМ равна
$$\sqrt{12^{2}-4^{2}}=8\sqrt{2}$$
Остается найти высоту ВВ1 из $\Delta BB_1 M$.

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\draw  [color={rgb, 255:red, 0; green, 0; blue, 0 }  ,draw opacity=1 ][line width=1.5] [line join = round][line cap = round] (156,52) .. controls (157.49,52) and (158.95,51.05) .. (160,50) ;
%Shape: Free Drawing [id:dp7862109430412447] 
\draw  [color={rgb, 255:red, 0; green, 0; blue, 0 }  ,draw opacity=1 ][line width=1.5] [line join = round][line cap = round] (161,49) .. controls (161,54.16) and (166.57,51.61) .. (165,49) .. controls (162.91,45.51) and (160,44.65) .. (160,49) ;
%Shape: Free Drawing [id:dp8747546430204128] 
\draw  [color={rgb, 255:red, 0; green, 0; blue, 0 }  ,draw opacity=1 ][line width=1.5] [line join = round][line cap = round] (271,113) .. controls (268.38,115.62) and (261.76,127.76) .. (265,131) ;
%Shape: Free Drawing [id:dp4403853008365548] 
\draw  [color={rgb, 255:red, 0; green, 0; blue, 0 }  ,draw opacity=1 ][line width=1.5] [line join = round][line cap = round] (235,114) .. controls (233.88,115.12) and (236.85,119.56) .. (239,121) .. controls (239.59,121.4) and (240.44,112.13) .. (239,115) .. controls (237.82,117.36) and (242,120.69) .. (242,123) ;
%Shape: Free Drawing [id:dp8865225127958187] 
\draw  [color={rgb, 255:red, 0; green, 0; blue, 0 }  ,draw opacity=1 ][line width=1.5] [line join = round][line cap = round] (244,114) .. controls (245.43,115.43) and (245,117.97) .. (245,120) .. controls (245,121.91) and (247.67,114.18) .. (250,120) .. controls (251.33,123.33) and (249.35,124) .. (247,124) ;
%Shape: Free Drawing [id:dp9755863354372275] 
\draw  [color={rgb, 255:red, 0; green, 0; blue, 0 }  ,draw opacity=1 ][line width=1.5] [line join = round][line cap = round] (243,113) .. controls (245.05,113) and (245.95,111) .. (248,111) ;
%Shape: Free Drawing [id:dp25477542858058044] 
\draw  [color={rgb, 255:red, 0; green, 0; blue, 0 }  ,draw opacity=1 ][line width=1.5] [line join = round][line cap = round] (250,109) .. controls (246.04,109) and (255.15,116.59) .. (253,108) .. controls (252.89,107.54) and (252.42,107.21) .. (252,107) .. controls (249.29,105.64) and (248,110.13) .. (248,112) ;

\end{tikzpicture}

\end{figure}

Отсюда $\mathbf{BB_1=8}.$

Задание 4, стр 60

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Задание 4, стр 60

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