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Giải bài 17 trang 75 sách bài tập toán 9 - Chân trời sáng tạo tập 1

Một du khách đếm được 645 bước chân khi đi từ ngay dưới chân toàn tháp thẳng ra phía ngoài cho đến vị trí có góc nhìn lên đỉnh là 45o (Hình 9). Tính chiều cao của tháp, biết rằng khoảng cách trung bình của mỗi bước chân là 0,4 m.

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

Toán - Văn - Anh
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Đề bài

Một du khách đếm được 645 bước chân khi đi từ ngay dưới chân toàn tháp thẳng ra phía ngoài cho đến vị trí có góc nhìn lên đỉnh là 45o𓆉 (Hình 9). Tính chiều cao của tháp, biết rằng khoảng cách trung bình của mỗi bước chân là 0,4 m.

 

Phương pháp giải - Xem chi tiết

Vận dụng tỉ số lượng giác của góc nhọn và hệ thức giữa cạnh và góc giúp giải tam giác vuông thuận lợi và nhanh chóng.

Lời giải chi tiết

💟Ta có chiều cao của toà tháp là AB, khoảng cách từ vị trí người đứng đến chân toà tháp là AC.

🥃Du khách đếm 645 bước chân khi đi từ A đến C và khoảng cách trung bình của mỗi bước chân là 0,4 m, suy ra AC = 645. 0,4 = 258 (m).

Xét tam giác ABC vuông tại A, ta có: AB = AC. tan \(\widehat {ACB}\)

Suy ra AB = 258. tan 45o = 258 (m).

Vậy toà tháp cao 258 m.

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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