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Giải bài 18 trang 80 SBT toán 10 - Cánh diều

Một người đi dọc bờ biển từ vị trí A đến vị trí B và quan sát một con tàu C đang neo đậu ngoài khơi.

𒁏Tổng 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

Một người đi dọc bờ biển từ vị trí A đến vị trí B và quan sát một con tàu C đang neo đậu ngoài khơi. Người đó tiến hành đo đạc và thu được kết quả: \(AB = 30m,\widehat {CAB} = {60^0},\widehat {CBA} = {50^0}\) (Hình 23). Tính khoảng cách từ vị trí A đến con tàu C🎶(làm tròn kết quả đến hàng phần mười theo đơn vị mét)?

Phương pháp giải - Xem chi tiết

Bước 1: Tính số đo góc \(\widehat {ACB}\) 

Bước 2:  Sử dụng định lí sin để tính độ dài AC của ∆ABC rồi kết luận

Lời giải chi tiết

Ta có:  🍰\(\widehat {ACB} = {180^0} - (\widehat {CBA} + \widehat {CAB}) = {70^0}\)

Áp dụng định lí sin cho ∆ABC꧂ ta có: \(\frac{{AC}}{{\sin \widehat {CBA}}} = \frac{{AB}}{{\sin \widehat {ACB}}} \Rightarrow AC = \frac{{AB.\sin \widehat {CBA}}}{{\sin \widehat {ACB}}} = \frac{{30.\sin {{50}^0}}}{{\sin {{70}^0}}} \approx 24,5\)

Vậy khoảng cách từ vị trí A đến con tàu C  là 24,5 m

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