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Giải bài 11 trang 75 SBT toán 10 - Cánh diều

Tàu A cách cảng C một khoảng 3 km và lệch hướng bắc một góc 47,450.

🌄Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Cánh diều

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

Tàu A cách cảng C một khoảng 3 km và lệch hướng bắc một góc 47,450. Tàu B cách cảng C một khoảng 5 km và lệch hướng bắc một góc 112,900ﷺ (Hình 11). Hỏi khoảng cách giữa hai tàu là bao nhiêu kilomet (làm tròn kết quả đến hàng phần trăm)?

Phương pháp giải - Xem chi tiết

Bước 1: Từ giả thiết xác định số đo các góc \(\widehat {NCA},\widehat {NCB},\widehat {ACB}\)

Bước 2: Áp dụng định lí cosin cho ∆ABC để tính độ dài AB rồi kết luận

Lời giải chi tiết

Theo giả thiết, \(\widehat {NCA} = 47,{45^0},\widehat {NCB} = 112,{90^0} \Rightarrow \widehat {ACB} = \widehat {NCB} - \widehat {NCA} = 65,{45^0}\)

Áp dụng định lí cosin cho ∆ABC ta có:

   \(A{B^2} = A{C^2} + B{C^2} - 2.AC.BC.\cos \widehat {ACB}\)\( \Rightarrow AB = \sqrt {A{C^2} + B{C^2} - 2.AC.BC.\cos \widehat {ACB}} \)                   \( = \sqrt {{3^2} + {5^2} - 2.3.5.\cos 65,{{45}^0}}  \approx 4,64\)Vậy khoảng cách giữa hai tàu là 4,64 km 

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