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Giải bài tập 4.28 trang 82 SGK Toán 9 tập 1 - Kết nối tri thức

Một cây cao bị gãy, ngọn cây đổ xuống mặt đất. Ba điểm: gốc cây, điểm gãy, ngọn cây tạo thành một tam giác vuông. Đoạn cây gãy tạo với mặt đất góc ({20^0}) và chắn ngang lối đi một đoạn 5 m (H.4.36). Hỏi trước khi bị gãy, cây cao khoảng bao nhiêu mét (làm tròn kết quả đến hàng phần mười)?

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

Toán - Văn - Anh
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Đề bài

Một cây cao bị gãy, ngọn cây đổ xuống mặt đất. Ba điểm: gốc cây, điểm gãy, ngọn cây tạo thành một tam giác vuông. Đoạn cây gãy tạo với mặt đất góc \({20^0}\) và chắn ngang lối đi một đoạn 5 m (H.4.36). Hỏi trước khi bị gãy, cây cao khoảng bao nhiêu mét (làm tròn kết quả đến hàng phần mười)?

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

ဣĐể tính chiều cao của cây ta cần tính độ dài của phần cây từ gốc đến điểm gãy và độ dài của phần cây từ điểm gãy đến ngọn cây rồi tính tổng.

🤡Để tính các độ dài trên ta sử dụng tỉ số lượng giác tan và định lý Pythagore

Lời giải chi tiết

Độ dài của phần từ gốc cây đến điểm gãy là \(5.\tan {20^0} \approx 1,8\) m Độ dài của phần cây từ điểm gãy đến ngọn cây là \(\sqrt {{5^2} + 1,{8^2}}  \approx 5,3\) m Trước khi bị gãy, chiều cao của cây khoảng \(1,8 + 5,3 = 7,1\) m

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