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Giải bài tập 11 trang 73 SGK Toán 9 tập 1 - Chân trời sáng tạo

Cho tam giác ABC vuông tại A. Chứng minh rằng (frac{{AC}}{{AB}} = frac{{sin B}}{{sin C}}).

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

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Đề bài

Cho tam giác ABC vuông tại A. Chứng minh rằng \(\frac{{AC}}{{AB}} = \frac{{\sin B}}{{\sin C}}\).

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

-  Đọc kĩ dữ liệu đề bài để vẽ hình -  Dựa vào tỉ số lượng giác của góc nhọn. Xét tam giác vuông, tỉ số giữa cạnh đối và cạnh huyền được gọi là sin, kí hiệu sin. -  Suy ra tỉ số cần tìm.

Lời giải chi tiết

Xét tam giác ABC vuông tại A, ta có: \(\sin B = \frac{{AC}}{{BC}}\) \(\sin C = \frac{{AB}}{{BC}}\) Suy ra: \(\frac{{\sin B}}{{\sin C}} = \frac{{AC}}{{BC}}:\frac{{AB}}{{BC}} = \frac{{AC}}{{BC}}.\frac{{BC}}{{AB}} = \frac{{AC}}{{AB}}\) (đpcm)

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