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Bài 8.46 trang 90 SGK Toán 11 tập 2 - Cùng khám phá

Cho hình chóp S.ABC có đáy ABC là tam giác vuông tại C, AC = a, BC = \(\sqrt 2 \)a, SA vuông góc với mặt phẳng đáy và SA = a.
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Đề bài

Cho hình chóp S.ABC có đáy ABC là tam giác vuông tại C, AC = a, BC = \(\sqrt 2 \)a, SA vuông góc với mặt phẳng đáy và SA = a. Góc giữa đường thẳng SB và mặt phẳng đáy bằng

A. 600.

B. 900.

C. 300.

D. 450.

Phương pháp giải - Xem chi tiết

Góc giữa d và (P): + Tìm giao điểm O của d và (P). + Từ A bất kì trên d, kẻ đường thẳng AA’ vuông góc xuống (P). + Góc AOA’ là góc cần tìm.

Lời giải chi tiết

Góc giữa đường thẳng SB và mặt phẳng đáy là \(\widehat {SBA}\)

\(AB = \sqrt {A{C^2} + B{C^2}}  = \sqrt {{a^2} + {{\left( {\sqrt 2 a} \right)}^2}}  = \sqrt 3 a\)

\(\tan \widehat {SBA} = \frac{{SA}}{{AB}} = \frac{1}{{\sqrt 3 }} \Rightarrow \widehat {SBA} = {30^0}\)Chọn đáp án C.

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

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