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dusya [7]
3 years ago
9

Triangle ABC is an equilateral triangle.Find the angle of rotation that maps A to B

Mathematics
1 answer:
svet-max [94.6K]3 years ago
3 0

The sum of the inner angles of any triangle is always 180°, i.e. you have


\alpha + \beta + \gamma = 180


In the particular case of an equilater triangle, all three angles are the same, so

\alpha = \beta = \gamma


and the expression becomes


\alpha + \beta + \gamma = \alpha + \alpha + \alpha = 3\alpha = 180


which implies \alpha = 60


So, if you rotate the triangle with respect to its center by 60 degrees, the triangle will map into itself. In particular, if you want point A to be mapped into point B, you have to perform a counter clockwise rotation of 60 degrees with respect to the center of the triangle.


Of course, this is equivalent to a clockwise rotation of 120 degrees.


Finally, both solutions admit periodicity: a rotation of 60+k360 degrees has the same effect of a rotation of 60 degrees, and the same goes for the 120 one (actually, this is obvisly true for any rotation!)

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