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Giải bài 2 trang 77 SGK Toán 10 tập 1 – Chân trời sáng tạo

Để lắp đường dây diện cao thế từ vị trí A đến vị trí B, do phải tránh một ngọn núi nên người ta phải nối đường dây từ vị trí A đến vị trí C dài 10 km, sau đó nối đường dây từ vị trí C đến vị trí B dài 8km. Góc tạo bởi hai đoạn dây AC và CB là 70. Tính chiều dài tăng thêm vì không thể nối trực tiếp từ A đến B.

Tổng hợp đề thi học kì 2 lớp 10 tấ🌸t cả các môn - Chân t﷽rời sáng tạo

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Đề bài

Để lắp đường dây diện cao thế từ vị trí A đến vị trí B, do phải tránh một ngọn núi nên người ta phải nối đường dây từ vị trí A đến vị trí C dài 10 km, sau đó nối đường dây từ vị trí C đến vị trí B dài 8km. Góc tạo bởi hai đoạn dây AC và CB là \({70^o}\). Tính chiều dài tăng thêm vì không thể nối trực tiếp từ A đến B.

Phương pháp giải - Xem chi tiết

Bước 1: Tính cạnh AB: Áp dụng định lí cosin: \(A{B^2} = B{C^2} + A{C^2} - 2.BC.AC.\cos C\) Bước 2: Tính chiều dài tăng thêm, bằng \(AC + CB - AB\)

Lời giải chi tiết

Áp dụng định lí cosin, ta có:\(\begin{array}{l}A{B^2} = B{C^2} + A{C^2} - 2.BC.AC.\cos C\\ \Leftrightarrow A{B^2} = {8^2} + {10^2} - 2.8.10.\cos {70^o}\\ \Rightarrow AB \approx 10,45\end{array}\)Vậy chiều dài tăng thêm vì không thể nối trực tiếp là:\(AC + CB - AB = 10 + 8 - 10,45 = 7,55\;(km).\)

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