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Giải bài tập 4.4 trang 73 SGK Toán 9 tập 1 - Kết nối tri thức

Cho hình chữ nhật có chiều dài và chiều rộng lần lượt là 3 và (sqrt 3 .) Tính góc giữa đường chéo và cạnh ngắn hơn của hình chữ nhật (sử dụng bảng giá trị lượng giác trang 69) .

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

Toán - Văn - Anh
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Đề bài

Cho hình chữ nhật có chiều dài và chiều rộng lần lượt là 3 và \(\sqrt 3 .\) Tính góc giữa đường chéo và cạnh ngắn hơn của hình chữ nhật (sử dụng bảng giá trị lượng giác trang 69) .

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Góc giữa cạnh ngắn hơn và đường chéo của hình chữ nhật chính là góc nhọn trong tam giác vuông khi biết cạnh đối và cạnh kề, ta sử dụng tỉ số lượng giác \(\tan ,\cot \)

Lời giải chi tiết

Xét hình chữ nhật EFHG có \(EG = FH = 3;EF = GH = \sqrt 3 \) Góc giữa đường chéo và cạnh ngắn hơn là góc FEH Ta có: \(\tan \widehat {FEH} = \frac{{FH}}{{EF}} = \frac{3}{{\sqrt 3 }} = \sqrt 3 \) nên \(\widehat {FEH} = {60^0}\) Vậy góc giữa đường chéo và cạnh ngắn hơn là \({60^0}.\)

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

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