In triangle ABC, AB = 10 and AC = 17. Let D be the foot of the perpendicular from A to BC. If BD:CD = 2:3, then find AD.
If BD:CD = 2:3, then find AD.
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\((10^2-h^2):(17^2-h^2)=4:9\\ 900-9h^2=1156-4h^2\\ -5h^2=256\)
The specified ratio BD: CD = 2: 3 is not possible.
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If BD:CD = 1:2, then find AD.
\(\overline {AD}=h\)
\((10^2-h^2):(17^2-h^2)=1:4\\ 400-4h^2=289-h^2\\ -3h^2=-111\\ h=\sqrt{37}\)
\(h=\overline{AD}=6.08\)
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