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Giải bài tập 4.27 trang 81 SGK Toán 9 tập 1 - Kết nối tri thức

Hình 4.35 là mô hình của một túp lều. Tìm góc (alpha ) giữa cạnh mái lều và mặt đất (làm tròn kết quả đến phút).

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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Đề bài

Hình 4.35 là mô hình của một túp lều. Tìm góc \(\alpha \) giữa cạnh mái lều và mặt đất (làm tròn kết quả đến phút).

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

ಌTa thấy các cạnh mái lều bằng nhau nên ta có một tam giác cân, đặt tên tam giác rồi ta có thể tính góc thông qua tỉ số lượng giác trong tam giác vuông.

🅠Chú ý: Đường trung tuyến trong tam giác cân vừa là đường cao vừa là đường phân giác.

Lời giải chi tiết

Xét tam giác ABC cân tại A, ta có AH vừa là đường cao vừa là đường trung tuyến nên H là trung điểm của đoạn BC Do đó \(HB = HC = \frac{{4,4}}{2} = 2,2\) m Tam giác AHC vuông tại H nên ta có: \(\tan \alpha  = \frac{{AH}}{{HC}} = \frac{{1,8}}{{2,2}} = \frac{9}{{11}}\) Do đó \(\alpha  \approx {39^0}17'\)

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