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Giải bài 6.25 trang 58 SGK Toán 8 - Cùng khám phá

Bạn Cường đo được khoảng cách từ vị trí mình đứng (điểm C) đến cây A và cây B
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Đề bài

Bạn Cường đo được khoảng cách từ vị trí mình đứng (điểm C) đến cây A và  cây B ở hai bên hồ nước lần lượt là \(AC = 24m\) và \(BC = 28m\) (Hình 6.66). Để tính độ dài \(AB,\) Cường xác định điểm \(D\) nằm giữa \(A,C\) và điểm \(E\) nằm giữa \(B,C\) sao cho \(CD = 6m,CE = 7m\) và đo khoảng cách giữa \(D\) và \(E.\) Nếu \(DE = 9m\) thì khoảng cách giữa \(A\) và \(B\) là bao nhiêu mét?

Phương pháp giải - Xem chi tiết

Áp dụng trường hợp đồng dạng cạnh góc cạnh: Nếu hai cạnh của tam giác này tỉ lệ với hai cạnh của tam giác kia và hai góc tạo bởi các cặp cạnh đó bằng nhau thì hai tam giác đồng dạng.

Lời giải chi tiết

Xét tam giác \(CDE\) và tam giác \(CAB\), ta có:\(\frac{{CD}}{{CA}} = \frac{{CE}}{{CB}} = \frac{1}{4}\)\(\widehat C\) chung=> \(\Delta CDE\) ∽ \(\Delta CAB\) (c-g-c)Ta có tỉ số đồng dạng:\(\begin{array}{l}\frac{{CD}}{{CA}} = \frac{{CE}}{{CB}} = \frac{{DE}}{{AB}}\\ \Leftrightarrow \frac{6}{{24}} = \frac{7}{{28}} = \frac{9}{{AB}}\\ \Rightarrow AB = 36\end{array}\)Vậy khoảng cách giữa A và B là 36 m.

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