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Giải bài 3 trang 74 vở thực hành Toán 9

Cho tam giác vuông có một góc nhọn ({30^o}) và cạnh đối với góc này bằng 5cm. Tính độ dài cạnh huyền của tam giác

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

Toán - Văn - Anh
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Đề bài

Cho tam giác vuông có một góc nhọn \({30^o}\) và cạnh đối với góc này bằng 5cm. Tính độ dài cạnh huyền của tam giác

Phương pháp giải - Xem chi tiết

Xét tam giác ABC vuông tại A có góc nhọn B bằng \(\alpha \). Ta có tỉ số giữa cạnh đối và cạnh huyền gọi là sin của \(\alpha \).

Lời giải chi tiết

(H.4.7)

Xét tam giác ABC vuông tại A, có \(AB = 5\), \(\widehat C = {30^o}\). Ta cần tính cạnh BC. Trong tam giác ABC vuông, ta có \(\sin C = \frac{{AB}}{{BC}}\), hay \(\sin {30^o} = \frac{{AB}}{{BC}}\), suy ra \(\frac{1}{2} = \frac{5}{{BC}}\), hay\(BC = 5:\frac{1}{2} = 10\left( {cm} \right)\)

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