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Giải bài tập 4.10 trang 78 SGK Toán 9 tập 1 - Kết nối tri thức

Tính góc nghiêng (alpha ) và chiều rộng AB của mái nhà kho trong Hình 4.23

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

Toán - Văn - Anh
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Đề bài

Tính góc nghiêng \(\alpha \) và chiều rộng AB của mái nhà kho trong Hình 4.23 (góc làm tròn đến độ, độ dài làm tròn đến dm)

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Để tính góc cần lập tỉ số lượng giác liên quan giữa cạnh đối và cạnh kề của tam giác vuông (\(\tan \alpha \)). Để tính cạnh AB ta có thể sử dụng định lý Pythagore

Lời giải chi tiết

Ta có: \(\tan \alpha  = \frac{{0,9}}{{15}}\) hay \(\alpha  \approx {3^0}\) Độ dài cạnh AB là \(AB = \sqrt {0,{9^2} + {{15}^2}}  = \sqrt {225,81}  \approx 15m = 150dm\)  Vậy góc nghiêng \(\alpha \) của mái nhà kho khoảng \({3^0}\) và chiều rộng \(AB\) khoảng \(150dm\)

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