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Giải bài 17 trang 80 SBT toán 10 - Cánh diều

Hai người A và B cùng quan sát một con tàu đang neo đậu ngoài khơi tại vị trí C.

🦄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

Hai người A và B cùng quan sát một con tàu đang neo đậu ngoài khơi tại vị trí C. Người A đứng trên bờ biển, người B đứng trên một hòn đảo cách bờ một khoảng AB🦩= 100 m. Hai người tiến hành đo đạc và thu được kết quả: \(\widehat {CAB} = {54^0},\widehat {CBA} = {74^0}\) (Hình 22). Hỏi con tàu cách hòn đảo bao xa (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 BC của ∆ABC rồi kết luận

Lời giải chi tiết

Ta có:  ꦏ\(\widehat {ACB} = {180^0} - (\widehat {CBA} + \widehat {CAB}) = {52^0}\)

Áp dụng định lí sin cho ∆ABCꦺ ta có: \(\frac{{BC}}{{\sin \widehat {CAB}}} = \frac{{AB}}{{\sin \widehat {ACB}}} \Rightarrow BC = \frac{{AB.\sin \widehat {CAB}}}{{\sin \widehat {ACB}}} = \frac{{100.\sin {{54}^0}}}{{\sin {{52}^0}}} \approx 102,7\)

Vậy con tàu cách hòn đảo 102,7 m

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Ph/hs Tham Gia Nhóm Để Cập Nhật Điểm Thi, Điểm Chuẩn Miễn Phí

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