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Bài 8.23 trang 79 SGK Toán 11 tập 2 - Cùng khám phá

Cho hình chóp S.ABCD có đáy ABCD là hình vuông cạnh bằng 1
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Đề bài

Cho hình chóp S.ABCD có đáy ABCD là hình vuông cạnh bằng 1. Tam giác SAB đều và nằm trong mặt phẳng vuông góc với mặt đáy (ABCD). Tỉnh khoảng cách từ B đến (SCD).

Phương pháp giải - Xem chi tiết

Tìm khoảng cách giữa M và (P): + Tìm (Q) chứa M và vuông góc với (P) theo giao tuyến d. + Từ M hạ MH vuông góc với d (H thuộc d). + Khi đó MH là khoảng cách cần tìm.

Lời giải chi tiết

Gọi H, M lần lượt là trung điểm của AB, CD. Kẻ HK vuông góc với SMVì AB // CD nên AB // (SCD)Do đó \(d\left( {B'\left( {SCD} \right)} \right) = d\left( {H;\left( {SCD} \right)} \right) = HK\)\(\begin{array}{l}\frac{1}{{H{K^2}}} = \frac{1}{{S{H^2}}} + \frac{1}{{H{M^2}}}\\ \Rightarrow HK = \frac{{\sqrt {21} }}{7}\end{array}\)

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