If you mean the use of similar triangles and the similarity of the linear dimensions of the shadows to calculate the linear dimensions of any object which can not be measured directly you need one indispensable condition to solve this problem.
This condition is the need for a parallel lines (such as directions to practically infinitely distant star) or lines which we can assume that in parallel with the permissible error of proportion (such as rays of the sun), Otherwise, if this condition is not feasible then due to parallax effects, the results of the calculations will be not reliable.
If this condition (the presence of parallel lines) is satisfied then we can measure with reasonable accuracy the length of the elements of imaginary triangles and applying one of the Thales theorems, to make a proportion and calculate the required interval (distance or height).
They are said to be similar but not congruent triangles.
They are similar triangles.
Two equilateral triangles are always similar!
There are no ratios that can be used for triangles that are not similar.
dilating them.
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Triangles are congruent if all three sides in one triangle are congruent to the corresponding sides in the other.When two triangles have corresponding sides with identical ratios, the triangles are similar.Of course if triangles are congruent, they are also similar.
They are said to be similar but not congruent triangles.
Pairs of triangles, in general, do not have to be similar.
They are similar triangles.
you measure both of their angles and see if they are the same i think.
Two equilateral triangles are always similar!
There are no ratios that can be used for triangles that are not similar.
why triangle are similar
Not always, sometimes two obtuse triangles are similar and sometimes they are not similar.
dilating them.
Dilating them