Bài 3:
a) Áp dụng HTL:
\(AH^2=BH.HC\Rightarrow y=\sqrt{9.16}=12\)
Áp dụng đ/lý Pytago:
\(\left\{{}\begin{matrix}AB^2=AH^2+BH^2\\AC^2=AH^2+HC^2\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=\sqrt{9^2+12^2}=15\\z=\sqrt{9^2+16^2}=\sqrt{337}\end{matrix}\right.\)
b) Áp dụng HTL:
\(AH^2=BH.HC\Rightarrow y=\dfrac{3^2}{2}=4,5\)
\(\left\{{}\begin{matrix}AB^2=AH^2+BH^2\\AC^2=AH^2+HC^2\end{matrix}\right.\)(Pytago)
\(\Rightarrow\left\{{}\begin{matrix}x=\sqrt{3^2+2^2}=\sqrt{13}\\z=\sqrt{3^2+13}=\sqrt{22}\end{matrix}\right.\)
Bài 4:
Áp dụng HTL:
\(AB^2=BH.BC\Rightarrow BH=\dfrac{3^2}{5}=1,8\)
\(HC=BC-BH=5-18=3,2\)
\(BC^2=AB^2+AC^2\)(Pytago)
\(\Rightarrow AC=\sqrt{BC^2-AB^2}=\sqrt{5^2-3^2}=4\)
\(AH^2=BH.HC\Rightarrow AH=\sqrt{BH.HC}=\sqrt{1,8.3,2}=2,4\)
