Giải bài tập 2 trang 92 SGK Toán 9 tập 1 - Cánh diều

Cho hình thoi (ABCD) có (AB = a,widehat {BAD} = 2alpha left( {0^circ < alpha < 90^circ } right)). Chứng minh: a) (BD = 2a.sin alpha ). b) (AC = 2a.cos alpha ).

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Đề bài

Cho hình thoi \(ABCD\) có \(AB = a,\widehat {BAD} = 2\alpha \left( {0^\circ < \alpha < 90^\circ } \right)\). Chứng minh: a) \(BD = 2a.\sin \alpha \). b) \(AC = 2a.\cos \alpha \).

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Lời giải chi tiết

Do \(\widehat {BAD} = 2\alpha\) nên \(\widehat {OAB} = \alpha \). a) Xét tam giác \(BOA\) vuông tại \(O\) có : \(BO = AB.\sin \alpha = a.\sin \alpha \). Mà \(BD = 2BO = 2a.\sin \alpha \). b) Xét tam giác \(BOA\) vuông tại \(O\) có: \(AO = AB.\cos \alpha = a.\cos \alpha \). Mà \(AC = 2AO = 2a.\cos \alpha \).

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🦩 Giải bài tập 3 trang 92 SGK Toán 9 tập 1 - Cánh diều Trong trò chơi xích đu ở Hình 41, khi dây căng xích đu (không dãn) (OA = 3m) tạo với phương thẳng đứng một góc là (widehat {AOH} = 43^circ ) thì khoảng cách (AH) từ em bé đến vị trí cân bằng là bao nhiêu mét (làm tròn kết quả đến hàng phần trăm)?
♈ Giải bài tập 4 trang 92 SGK Toán 9 tập 1 - Cánh diều Một người đứng ở vị trí (B) trên bờ sông muốn sử dụng la bàn để ước lượng khoảng cách từ vị trí đó đến một vị trí (A) ở trên một cù lao giữa dòng sông. Người đó đã làm như sau: - Sử dụng la bàn, xác định được phương (BA) lệch với phương Nam – Bắc về hướng Đông (52^circ ). - Người đó di chuyển đến vị trí (C), cách (B) một khoảng là 187m. Sử dụng la bàn, xác định được phương (CA) lệch với phương Nam – Bắc về hướng Tây (27^circ ); (CB) lệch với phương Nam – Bắc về hướng Tây
𝓀 Giải bài tập 1 trang 92 SGK Toán 9 tập 1 - Cánh diều Cho tam giác (ABC) vuông tại (A) có đường cao (AH) và (widehat B = alpha ) (Hình 40). a) Tỉ số (frac{{HA}}{{HB}}) bằng: A. (sin alpha ). B. (cos alpha ). C. (tan alpha ). D. (cot alpha ). b) Tỉ số (frac{{HA}}{{HC}}) bằng: A. (sin alpha ). B. (cos alpha ). C. (tan alpha ). D. (cot alpha ). c) Tỉ số (frac{{HA}}{{AC}}) bằng: A. (sin alpha ). B. (cos alpha ). C. (tan alpha ). D. (cot alpha ).

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Giải bài tập 2 trang 92 SGK Toán 9 tập 1 - Cánh diều

Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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