Question

Giúp mình câu 42 với. Xin cảm ơn

Answer 1

\(\left\{{}\begin{matrix}A'B'\perp AA'\\A'B'\perp A'C'\end{matrix}\right.\) \(\Rightarrow A'B'\perp\left(ACC'A'\right)\)

\(\Rightarrow\widehat{B'CA'}\) là góc giữa \(B'C\) và (ACC'A') \(\Rightarrow sin\widehat{B'CA'}=\dfrac{A'B'}{B'C}=\dfrac{1}{2\sqrt{5}}\)

Mặt khác:

 \(CC'||AA'\Rightarrow CC'||\left(ABB'A'\right)\Rightarrow d\left(A'B;CC'\right)=d\left(CC';\left(ABB'A'\right)\right)=d\left(C;\left(ABB'A'\right)\right)=AC\)

\(\Rightarrow AC=a\sqrt{3}\Rightarrow AB=AC.tan30^0=a\)

\(\Rightarrow B'C=2\sqrt{5}A'B'=2a\sqrt{5}\) ; \(BC=\dfrac{AB}{sin30^0}=2a\)

\(\Rightarrow BB'=\sqrt{B'C^2-BC^2}=4a\)

\(V=\dfrac{1}{2}AB.AC.BB'=2a^3\sqrt{3}\)