How to construct $\Delta ABC$ given $a$, height from $A$ on $BC$ and A$B:AC$.
How to construct $\Delta ABC$ given $a$, height from $A$ on $BC$ and A$B:AC$.
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geometry
geometric-construction
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0I think there are 2,1 or 0 possible triangles you can build with these data – 2017-02-18
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0However, https://en.wikipedia.org/wiki/Circles_of_Apollonius is really useful in this case – 2017-02-18
1 Answers
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If the ratio $\frac{AB}{AC}$ is known, then $A$ belong to an Apollonius circle relative to the segment $BC=a$, hence the problem can be solved by intersecting a line parallel to $BC$ with the previous circle. Here it is an explicit solution for $BC=4$, $\frac{AB}{AC}=\frac{2}{3}$ and $h_a=3$:
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1Nice link. (+1) – 2017-02-18