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Giải bài 4 trang 88 sách bài tập toán 8 - Cánh diều

Cho tam giác \(ABC\) vuông cân tại \(A\) có độ dài cạnh góc vuông \(AB\) và \(AC\) là 4 cm. Kẻ đường cao \(AD\) của tam giác \(ABC\).

ဣTổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Cánh diều

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

Cho tam giác \(ABC\) vuông cân tại \(A\) có độ dài cạnh góc vuông \(AB\) và \(AC\) là 4 cm. Kẻ đường cao \(AD\) của tam giác \(ABC\). a)     Tính độ dài cạnh đáy \(BC\)(làm tròn kết quả đến hàng phần trăm của centimet) b)    Tính độ dài đường cao \(AD\) (làm tròn kết quả đến hàng phần trăm của centimet)

Phương pháp giải - Xem chi tiết

Áp dụng định lí Pythagore trong tam giác vuông: Trong một tam giác vuông, bình phương của cạnh huyền bằng tổng bình phương hai cạnh góc vuông.

Lời giải chi tiết

a)     Áp dụng định lí Pythagore ta có:\(B{C^2} = A{B^2} + A{C^2} = 32\)Suy ra \(BC = \sqrt {32}  \approx 5,66\left( {cm} \right)\)b)    Lại có \(\Delta ABD = \Delta ACD\) (cạnh huyền-cạnh góc vuông)Suy ra \(BD = CD\). Vậy \(D\) là trung điểm của \(BC\).Do đó \(CD = \frac{{BC}}{2} = \frac{{\sqrt {32} }}{2} \approx 2,83\left( {cm} \right)\)Tam giác \(ACD\) vuông tại \(D\) nên ta tính được \(AD \approx 2,83\left( {cm} \right)\).

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