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Giải bài 6.33 trang 65 SGK Toán 8 - Cùng khám phá

Trong Hình 6.87, khi bạn An đứng ở vị trí điểm \(A\),
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Đề bài

Trong Hình 6.87, khi bạn An đứng ở vị trí điểm \(A\), An thấy bức tường \(ST\) vừa che khuất ngôi nhà phía sau. Biết khoảng cách từ mắt An đến mặt đất là 1,5 , chiều cao của bức tường là 3 m, khoảng cách từ An đến bức tường là 0,8 m và khoảng cách từ bức tường đến ngôi nhà là 2 m. Tính chiều cao của ngôi nhà.

Phương pháp giải - Xem chi tiết

Nếu một góc nhọn của tam giác vuông này bằng một góc nhọn của tam giác vuông kia thì hai tam giác vuông đó đồng dạng.

Lời giải chi tiết

Kẻ \(BQ \bot MN\) cắt \(ST\) tại \(P\), cắt \(MN\) tại \(Q\).Xét tam giác \(BPS\) và tam giác \(BQM\), ta có:\(\widehat {BPS} = \widehat {BQM} = 90^\circ \)\(\widehat B\) là góc chung=> \(\Delta BPS\)∽\(\Delta BQM\) (góc nhọn-góc vuông)Ta có tỉ số đồng dạng:\(\begin{array}{l}\frac{{SP}}{{MQ}} = \frac{{BP}}{{BQ}}\\\frac{{3 - 1,5}}{{MQ}} = \frac{{0,8}}{{0,8 + 2}}\\ \Rightarrow MQ = 5,25\end{array}\)Mà \(MN = MQ + QN = 5,25 + 1,5 = 6,75\)Vậy chiều cao ngôi nhà là 6,75 m.

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