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Giải bài 3 trang 72 SGK Toán 10 tập 1 – Chân trời sáng tạo

Cho tam giác ABC, biết cạnh. Tính các góc, các cạnh còn lại và bán kính đường tròn ngoại tiếp của tam giác đó.

Tổng hợp đề thi học kì☂ 2 lớp 10 tất cả các môn - Chân trời sáng tạo

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Đề bài

Cho tam giác ABC, biết cạnh \(a = 152,\;\widehat B = {79^o},\;\widehat C = {61^o}.\) Tính các góc, các cạnh còn lại và bán kính đường tròn ngoại tiếp của tam giác đó.

Phương pháp giải - Xem chi tiết

Áp dụng định lí sin: \(\frac{a}{{\sin A}} = \frac{b}{{\sin B}} = \frac{c}{{\sin C}} = 2R\)

Lời giải chi tiết

 

Đặt \(AB = c,AC = b,BC = a.\)Ta có: \(a = 152;\widehat A = {180^o} - ({79^o} + {61^o}) = {40^o}\)Áp dụng định lí sin, ta có:\(\frac{a}{{\sin A}} = \frac{b}{{\sin B}} = \frac{c}{{\sin C}} = 2R\)Suy ra:\(\begin{array}{l}AC = b = \frac{{a.\sin B}}{{\sin A}} = \frac{{152.\sin {{79}^o}}}{{\sin {{40}^o}}} \approx 232,13\\AB = c = \frac{{a.\sin C}}{{\sin A}} = \frac{{152.\sin {{61}^o}}}{{\sin {{40}^o}}} \approx 206,82\\R = \frac{a}{{2\sin A}} = \frac{{152}}{{2\sin {{40}^o}}} \approx 118,235\end{array}\)

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