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Giải bài tập 4.9 trang 86 SGK Toán 9 tập 1 - Cùng khám phá

Tính độ dài cạnh bên CD của hình thang ABCD trong Hình 4.24.

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Đề bài

Tính độ dài cạnh bên CD của hình thang ABCD trong Hình 4.24.

Phương pháp giải - Xem chi tiết

+ Kẻ DK vuông góc với BC tại K. + Tam giác AHB vuông tại H nên \(AH = AB.\sin B\). + Chứng minh tứ giác AHKD là hình bình hành. Do đó, \(HK = AD = 10,DK = AH\). + Áp dụng định lí Pythagore vào tam giác DKC vuông tại K để tính CD.

Lời giải chi tiết

Kẻ DK vuông góc với BC tại K. \(\Delta \)AHB vuông tại H nên \(AH = AB.\sin B = 9.\sin {66^o} \approx 8,2\) \(BH = AB.\cos B = 9.\cos {66^o} \approx 3,7\) Tứ giác AHKD có: AD//HK (gt), AH//DK (cùng vuông góc với BC) nên tứ giác AHKD là hình bình hành. Do đó, \(HK = AD = 10,DK = AH \approx 8,2\). Độ dài đoạn thẳng KC là: \(KC = BC - BH - HK \approx 21 - 3,7 - 10 = 7,3\) \(\Delta \)DKC vuông tại K nên \(D{C^2} = D{K^2} + K{C^2} \approx 8,{2^2} + {7,3^2} = 120,53\) (Định lí Pythagore) nên \(DC \approx 11\).

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