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Giải bài 14 trang 74 sách bài tập toán 9 - Chân trời sáng tạo tập 1

Giải các tam giác vuông trong Hình 7.

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

Toán - Văn - Anh
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Đề bài

Giải các tam giác vuông trong Hình 7.

 

Phương pháp giải - Xem chi tiết

Giải tam giác vuông là tính các cạnh và các góc chưa biết của tam giác đó. 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) \(\widehat C = {90^o} - {15^o} = {75^o};\) \(AB = 5.\cot {15^o} \approx 18,66;\) \(BC = \frac{5}{{\sin {{15}^o}}} \approx 19,32;\) b) \(\widehat A = {90^o} - {32^o} = {58^o};\) \(AC = 56.\sin {32^o} \approx 29,68;\) \(BC = 56.c{\rm{os3}}{{\rm{2}}^o} \approx 47,49;\) c) \(BC = \sqrt {A{B^2} - A{C^2}}  = \sqrt {{{25}^2} - {{20}^2}}  = 15;\) \(\sin A = \frac{{15}}{{25}} = \frac{3}{5}\), suy ra \(\widehat A \approx {36^o}52';\) \(\sin B = \frac{{20}}{{25}} = \frac{4}{5},\) suy ra \(\widehat B \approx {53^o}8'\).

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

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