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Giải bài 4 trang 81 sách bài tập toán 10 - Chân trời sáng tạo

a) Diện tích tam giác ABC b) Bán kính đường tròn ngoại tiếp và bán kính đường tròn nội tiếp tam giác ABC

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

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

Cho \(\Delta ABC\) có \(\widehat A = 99^\circ ,b = 6,c = 10\). Tính:

a) Diện tích tam giác ABC

b) Bán kính đường tròn ngoại tiếp và bán kính đường tròn nội tiếp tam giác ABC

Lời giải chi tiết

a) Áp dụng định lí sin vào tam giác ABC ta có:\({S_{ABC}} = \frac{1}{2}bc\sin A = \frac{1}{2}.6.10.\sin 99^\circ  \simeq 29,63\) (đvdt)b) Áp dụng định lí côsin ta tính được:\(a = \sqrt {{b^2} + {c^2} - 2bc\cos A}  = \sqrt {{6^2} + {{10}^2} - 2.6.10\cos 99^\circ }  \simeq 12,44\)Bán kính đường tròn ngoại tiếp tam giác ABC là:\(R = \frac{{abc}}{{4S}} \simeq \frac{{12,44.6.10}}{{4.29,63}} \simeq 6,25\)Bán kính đường tròn nội tiếp tam giác là:\(r = \frac{S}{p} = \frac{{29,63}}{{\frac{{\left( {12,44 + 6 + 10} \right)}}{2}}} \simeq 2,084\)

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Ph/hs Tham Gia Nhóm Để Cập Nhật Điểm Thi, Điểm Chuẩn Miễn Phí

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