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Bài 8.40 trang 89 SGK Toán 11 tập 2 - Cùng khám phá

Cho hình lăng trụ ABC.A’B’C’ có đáy ABC là tam giác đều cạnh a.
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Đề bài

Cho hình lăng trụ ABC.A’B’C’ có đáy ABC là tam giác đều cạnh a. Góc tạo bởi cạnh bên và mặt đáy bằng 600ဣ. Hình chiếu của A trên mặt phẳng (A’B’C’) là trung điểm H của cạnh B’C’.

a ) Tính khoảng cách giữa hai mặt đáy của hình lăng trụ này. b) Tính số đo của góc nhị diện tạo bởi mặt bên (ABB’A’) và mặt đáy (A’B’C’).

Phương pháp giải - Xem chi tiết

Tìm a, b lần lượt vuông góc với (P) và (Q) thì góc giữa a và b là góc giữa (P) và (Q).

Lời giải chi tiết

a) Góc giữa AA’ và (A’B’C’) là góc AA’H. Suy ra \(\widehat {AA'H} = {60^0}\)Tam giác A’B’C’ đều cạnh a nên A’H = \(\frac{{\sqrt 3 }}{2}a\)\(AH = A'H.\tan {60^0} = \frac{{\sqrt 3 }}{2}a.\sqrt 3  = \frac{3}{2}a\)b) Gọi D là trung điểm A’B’Góc giữa (ABB’A’) và (A’B’C’) là góc ADC’.

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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