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Giải bài 16 trang 79 SBT toán 10 - Cánh diều

Gia đình bạn An sở hữu một mảnh đất hình tam giác. Chiều dài của hàng rào MN là 150 m, chiều dài của hàng rào MP là 230 m

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

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

Gia đình bạn An sở hữu một mảnh đất hình tam giác. Chiều dài của hàng rào MN là 150 m, chiều dài của hàng rào MP là 230 m. Góc giữa hai hàng rào MN và MP là 1100 (Hình 21)

a) Diện tích mảnh đất mà gia đình bạn An sở hữu là bao nhiêu mét vuông (làm tròn kết quả đến hàng phần mười)?

b) Chiều dài hàng rào NPꦺ là bao nhiêu mét (làm tròn kết quả đến hàng phần mười)?

Phương pháp giải - Xem chi tiết

Bước 1: Sử dụng công thức diện tích \(S = \frac{1}{2}MN.MP\sin M\) để tính diện tích ∆MNP

Bước 2: Sử dụng định lí cosin để tính độ dài NP

Bước 3: Kết luận

Lời giải chi tiết

a) \({S_{MNP}} = \frac{1}{2}MN.MP\sin M = \frac{1}{2}.150.230.\sin {110^0} \approx 16209,7\) (m2)

Vậy diện tích mảnh đất mà gia đình bạn An sở hữu là 16209,7 m2

b) Áp dụng định lí cosin cho ∆ABCౠ ta có: \(N{P^2} = M{N^2} + M{P^2} - 2.MN.MP.\cos M\)

\( \Rightarrow NP = \sqrt {M{N^2} + M{P^2} - 2.MN.MP.\cos M} \)\( = \sqrt {{{150}^2} + {{230}^2} - 2.150.230.\cos {{110}^0}}  \approx 314,6\)(m)

Vậy chiều dài hàng rào NP là 314,6 m

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