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Giải bài 4.34 trang 52 sách bài tập toán 9 - Kết nối tri thức tập 1

Một cầu thủ đứng cách khung thành 18m, đá quả bóng sát mặt đất, nghiêng một góc ({20^o}) so với phương vuông góc với khung thành, tới điểm M của khung thành (H.4.19). Tính khoảng cách từ cầu thủ đến điểm M (làm tròn đến dm).

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

Toán - Văn - Anh
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Đề bài

Một cầu thủ đứng cách khung thành 18m, đá quả bóng sát mặt đất, nghiêng một góc \({20^o}\) so với phương vuông góc với khung thành, tới điểm M của khung thành (H.4.19). Tính khoảng cách từ cầu thủ đến điểm M (làm tròn đến dm).

Phương pháp giải - Xem chi tiết

Xét tam giác ABC vuông tại A có góc nhọn B bằng \(\alpha \) thì tỉ số giữa cạnh kề và cạnh huyền gọi là côsin của \(\alpha \)

Lời giải chi tiết

Gọi H là hình chiếu vuông góc của cầu thủ đứng tại A lên đường thẳng chứa khung thành thì ta được tam giác AHM vuông tại H, \(AH = 18m,\widehat {HAM} = {20^o}\). Tam giác AHM vuông tại H nên \(\cos \widehat {HAM} = \frac{{AH}}{{AM}}\) nên \(AM = \frac{{AH}}{{\cos \widehat {HAM}}} = \frac{{18}}{{\cos {{20}^o}}} \approx 19,2\left( m \right) = 192dm\).

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

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