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Giải bài 9.47 trang 111 SGK Toán 8 tập 2 - Kết nối tri thức

Để tính được chiều cao gần đúng của kim tự tháp Ai Cập

ꦕTổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

🐟Để tính được chiều cao gần đúng của kim tự tháp Ai Cập, người ta nắm 1 cây cọc cao 1m vuông góc với mặt đất và đo được bóng cây cọc trên mặt đất là 1,5m. Khi đó chiều dài bóng của kim tự tháp trên mặt đất là 208,2 m. Hỏi kim tự tháp cao bao nhiêu mét?

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Chứng minh ΔB'A'C' ∽ ΔBAC từ đó suy ra tỉ số và tính AB

Lời giải chi tiết

Ta có hình vẽ:

 

Vì trong cùng một thời điểm, các tia nắng mặt trời tạo với mặt đất các góc bằng nhau => \(\widehat {BAC} = \widehat {B'A'C'}\) - Xét hai tam giác vuông BAC (vuông tại B) và tam giác B'A'C' (vuông tại B') có: \(\widehat {BAC} = \widehat {B'A'C'}\)

=> ΔB'A'C' ∽ ΔBAC

=> \(\frac{{A'B'}}{{AB}} = \frac{{B'C'}}{{BC}}\) => \(\frac{1}{{AB}} = \frac{{1,5}}{{208,2}}\) => AB=138,8m

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