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Giải bài 10 trang 81 sách bài tập toán 10 - Chân trời sáng tạo

Độ dài lớn nhất của đoạn OB bằng:

🥀Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Chân trời sáng tạo

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

Cho \(\widehat {xOy} = 30^\circ \). Gọi A và B là hai điểm di động lần lượt trên Ox và Oy sao cho \(AB = 1\). Độ dài lớn nhất của đoạn OB bằng:

A. 1,5  B. \(\sqrt 3 \)    C. \(2\sqrt 2 \)  D. 2

Phương pháp giải - Xem chi tiết

Áp dụng định lí sin trong tam giác OAB để tính OB.

Lời giải chi tiết

Ta có: \(\frac{{AB}}{{\sin O}} = \frac{{OB}}{{\sin A}} \Rightarrow OB = \sin A.\frac{1}{{\sin {{30}^ \circ }}} = 2\sin A \le 2\)Dấu bằng xảy ra khi \(\sin A = 1\) hay \(AB \bot Oy\)Chọn D.

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

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