The triangle is determined with three points: $A(1, -2, 8), B(0, 0, 4), C(6, 2, 0)$. How do I calculate its surface and altitude from B?
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What did you try? What are your thoughts? Do you know about the scalar product? – Ewan Delanoy Aug 28 '18 at 08:34
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1popular question: https://math.stackexchange.com/questions/128991/how-to-calculate-area-of-3d-triangle – farruhota Aug 28 '18 at 08:51
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Once you have the area using any of the methods in the linked question above, divide by $AC$ to get the altitude. – amd Aug 28 '18 at 19:55
1 Answers
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HINT
We can proceed as follow
consider the line $l_{AC}$ and a generic point $P\in l_{AC}$
consider the line $l_{BP}$ and find $\bar P$ such that $l_{B\bar P}\perp l_{AC}$ by the condition
$$v_{B\bar P}\cdot v_{AC}=0$$
- then the height is $B\bar P$ and the area is $S=\frac12 AC\cdot B\bar P$
As an alternative
- find the lenght $AB$, $BC$, $AC$ and the area by Heron's formula
- from $S=\frac12 AC \cdot H_B$ find $H_B$
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