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Giải bài 9.32 trang 109 SGK Toán 8 tập 2 - Kết nối tri thức

Cho tam giác ABC vuông tại A và có đường cao AH

𝓀Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

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

Cho tam giác ABC vuông tại A và có đường cao AH. Biết rằng BH=16cm, CH=9cm a) Tính độ dài đoạn thẳng AH b) Tính độ dài đoạn thằng AB và AC

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Áp dụng định lý Pythagore

Lời giải chi tiết

a) Có BC=BH+CH=16+9=25 Xét tam giác AHC vuông tại H có: \(A{H^2} = A{C^2} - C{H^2}\)(định lý Pythagore) (1) Xét tam giác AHB vuông tại H có: \(A{H^2} = A{B^2} - B{H^2}\) (định lý Pythagore) (2) Xét (1) + (2), có: \(\begin{array}{l}2{\rm{A}}{H^2} = A{C^2} - C{H^2} + A{B^2} - B{H^2}\\2{\rm{A}}{H^2} = B{C^2} - C{H^2} - B{H^2}\\2{\rm{A}}{H^2} = {25^2} - {9^2} - {16^2}\\2{\rm{A}}{H^2} = 288\end{array}\) AH=12(cm) b) Có \(A{C^2} = A{H^2} + C{H^2}\) (định lý Pythagore)  => \(A{C^2} = {12^2} + {9^2} = 225\) => AC=15(cm) Có  \(A{B^2} = A{H^2} + B{H^2}\) (định lý Pythagore)  => \(A{B^2} = {12^2} + {16^2} = 400\) => AB=20(cm)

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