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Bài 2 trang 86 SGK Toán 11 tập 2 – Chân trời sáng tạo

Cho hình chóp \(S.ABCD\) có đáy \(ABCD\) là hình vuông cạnh \(b\), \(SA\) vuông góc với mặt đáy, \(SC = 2b\sqrt 2 \).

ꦜTổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Cho hình chóp \(S.ABCD\) có đáy \(ABCD\) là hình vuông cạnh \(b\), \(SA\) vuông góc với mặt đáy, \(SC = 2b\sqrt 2 \). Số đo góc giữa cạnh bên \(SC\) và mặt đáy là A. \({60^ \circ }\). B. \({30^ \circ }\). C. \({45^ \circ }\). D. \({50^ \circ }\).

Phương pháp giải - Xem chi tiết

Cách tính góc giữa đường thẳng và mặt phẳng: Tính góc giữa đường thẳng đó và hình chiếu của nó lên mặt phẳng.

Lời giải chi tiết

\(SA \bot \left( {ABCD} \right) \Rightarrow \left( {SC,\left( {ABCD} \right)} \right) = \left( {SC,AC} \right) = \widehat {SCA}\)\(ABCD\) là hình vuông \( \Rightarrow AC = \sqrt {A{B^2} + B{C^2}}  = b\sqrt 2 \)\(\cos \widehat {SCA} = \frac{{AC}}{{SC}} = \frac{1}{2} \Rightarrow \widehat {SCA} = {60^ \circ }\)Vậy \(\left( {SC,\left( {ABCD} \right)} \right) = {60^ \circ }\)Chọn A.

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