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Giải bài 9.28 trang 103 SGK Toán 8 tập 2 - Kết nối tri thức

Một người ở vị trí điểm A muốn đo khoảng cách đến điểm B ở bên kia sông

ꦉTổng 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

♈Một người ở vị trí điểm A muốn đo khoảng cách đến điểm B ở bên kia sông mà không thể qua sông được. Sử dụng giác kế, người đó xác định được một điểm M trên bờ sông sao cho AM = 2 m, AM vuông góc với AB và đo được số đo góc AMB. Tiếp theo, người đó vẽ trên giấy tam giác A'M'B' vuông tại A' có AM' = 1cm, \(\widehat {A'M'B'} = \widehat {AMB}\) và đo được A'B' = 5 cm (H.9.56). Hỏi khoảng cách từ A đến B là bao nhiêu mét?

 

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

🌸Chứng minh ΔA′M′B′ ∽ ΔAMB rồi suy ra các tỉ số và tính AB

Lời giải chi tiết

Xét  ΔA′M′B′ (vuông tại A) và ΔAMB (vuông tại A') có \(\widehat {A'M'B'} = \widehat {AMB}\)

=> ΔA′M′B′ ∽ ΔAMB

=> \(\frac{{A'M'}}{{AM}} = \frac{{A'B'}}{{AB}}\) => \(\frac{1}{2} = \frac{5}{{AB}}\) => AB=10 (m)

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