MC ⊥ (ABC) |
CD ⊥ AD | => MC ⊥ AD => d(M,AD)=MD
AD ⊂ (ABC) |
In Δ ABC , [tex] BC^{2}= AC^{2}+ AB^{2} [/tex]
[tex] BC^{2}= 40^{2}+ 30^{2}
= 1600+900
= 2 500 =\ \textgreater \ BC= \sqrt{2 500}=\ \textgreater \ BC= 50[/tex]cm
AD-inaltime in ΔABC => AD=[tex] \frac{AC*AB}{BC}= \frac{40*30}{50}= \frac{1200}{50}= 24[/tex]cm
In ΔACD ,[tex] CD^{2}= AC^{2}- AD^{2} [/tex]
[tex] CD^{2}= 40^{2} - 24^{2}
=1 600- 576
=1024 =\ \textgreater \ CD= \sqrt{1024}=\ \textgreater \ CD= 32[/tex] cm
In ΔMCD , [tex] MD^{2}= MC^{2}+ CD^{2}
= 24^{2}+ 32^{2}
=576+ 1024
= 1600 [/tex] => MD=[tex] \sqrt{1600}=40cm [/tex]
b)
MC⊥(ABC) |
CA⊥AB | => MA ⊥ AB => d(M,AB)=MA
AB⊂(ABC) |
In ΔMCA , [tex] MA^{2}= MC^{2}+ CA^{2} [/tex]
[tex] MA^{2}= 24^{2} + 40^{2}
=576 + 1600
=MA= \sqrt{2176} = 8 \sqrt{34}cm [/tex]
