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Giải bài tập 6 trang 79 SGK Toán 9 tập 2 - Cánh diều

Khung thép của một phần sân khấu có dạng đường tròn bán kính 15m. Mắt của một người thợ ở vị trí A nhìn hai đèn ở các vị trí B, C (A, B, C cùng thuộc đường tròn bán kính 15m), bằng cách nào đó, người thợ thấy rằng góc nhìn (widehat {BAC} = 30^circ ) (hình 31). Khoảng cách giữa hai vị trí B và C bằng bao nhiêu mét?

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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Đề bài

Khung thép của một phần sân khấu có dạng đường tròn bán kính 15m. Mắt của một người thợ ở vị trí A nhìn hai đèn ở các vị trí B, C (A, B, C cùng thuộc đường tròn bán kính 15m), bằng cách nào đó, người thợ thấy rằng góc nhìn \(\widehat {BAC} = 30^\circ \) (hình 31). Khoảng cách giữa hai vị trí B và C bằng bao nhiêu mét?

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Bước 1: Tính số đo góc BOC. Bước 2: Chứng minh tam giác BOC đều. Bước 3: Tính BC (= R)

Lời giải chi tiết

Bài toán được mô tả bằng hình vẽ sau:

Trong đó: \(\widehat {BAC} = 30^\circ ,BO = OC = R = 15m.\) Xét (O): góc BAC là góc nội tiếp chắn cung BC nên \(\widehat{BAC}=\frac{1}{2}sđ\overset\frown{BC}=30{}^\circ \) do đó \(sđ\overset\frown{BC}=60{}^\circ \). Góc BOC là góc ở tâm chắc cung BC của (O) nên \(\widehat{BOC}=sđ\overset\frown{BC}=60{}^\circ \). Xét tam giác BOC có: BO = CO (= R) \(\widehat {BOC} = 60^\circ \) Nên tam giác BOC đều suy ra BO = CO = BC = 15m. Vậy khoảng cách giữa B và C là 15m.

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