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Giải bài 15 trang 75 sách bài tập toán 9 - Chân trời sáng tạo tập 1

Cho tam giác ABC có AB = 15 cm, BC = 20 cm, (widehat {ABC} = {64^o}). Tính độ dài: a) đường cao AH; b) các đoạn thẳng BH, CH; c) cạnh AC

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

Toán - Văn - Anh
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Đề bài

Cho tam giác ABC có AB = 15 cm, BC = 20 cm, \(\widehat {ABC} = {64^o}\). Tính độ dài:

a) đường cao AH;

b) các đoạn thẳng BH, CH;

c) cạnh AC

Phương pháp giải - Xem chi tiết

Vận dụng tỉ số lượng giác của góc nhọn và hệ thức giữa cạnh và góc giúp giải tam giác vuông thuận lợi và nhanh chóng.

Lời giải chi tiết

a) AH = AB. sin \(\widehat {ABC}\) = \(15.\sin {64^o} \approx 13,48(cm)\) b) BH = AB. \(\cos \widehat {ABC} = 15.\cos {64^o} \approx 6,58(cm)\); CH = BC – BH \( \approx 20 - 6,58 = 13,42(cm)\); c) \(AC = \sqrt {A{H^2} + C{H^2}}  \approx \sqrt {{{13,48}^2} + {{13,42}^2}}  \approx 19,02(cm).\)

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