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Giải bài 7 trang 75 SBT toán 10 - Cánh diều

Cho tam giác ABC có \(AB = 5,AC = 7,BC = 9\). Tính số đo góc A và bán kính R của đường tròn ngoại tiếp tam giác ABC (làm tròn kết quả đến hàng phần mười)

Tổng hợp🍃 đề thi học kì 2 lớp 10 tất cả các môn - Cánh diều

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Đề bài

Cho tam giác ABC có \(AB = 5,AC = 7,BC = 9\). Tính số đo góc A và bán kính R của đường tròn ngoại tiếp tam giác ABC (làm tròn kết quả đến hàng phần mười)

Phương pháp giải - Xem chi tiết

Bước 1:  Sử dụng định lí cosin để tính góc A

Bước 2: Sử dụng định lí sin để tính bán kính R

Lời giải chi tiết

Áp dụng định lí cosin cho ∆ABC ta có: \(B{C^🍨2} = A{B^2} + A{C^2} - 2.AB.AC.\cos A\)

\( \Rightarrow \cos A = \frac{{A{B^2} + A{C^2} - B{C^2}}}{{2.AB.AC}} = \frac{{{5^2} + {7^2} - {9^2}}}{{2.5.7}} =  - \frac{1}{{10}}\) \( \Rightarrow \widehat A \approx {96^0}\)

Áp dụng định lí sin cho ∆ABC ta có: \(\frac{{BC}}{{\sin {\rm{A}}}} = 2R \Righ𒊎tarrow R = \frac{{BC}}{{2\sin {\rm{A}}}} = \frac{9}{{2.\sin {{96}^0}}} \approx 4,5\)

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