A Hard Triangle Problem
Geometry
Level
3
Given an isosceles right triangle ABC at A. AH is the altitude of the triangle ABC. Draw a point M on BC. From M, draw MD and ME perpendicular to AB and AC, respectively. Calculate the angle in degrees.
The answer is 45.
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1 solution
By construction with 2 perpendicular lines were creating a similar (precise: reflected) triangle of the original one. The desired angle is the same, as one of the non-right angles of the original triangle (90,45,45) -> 4 5 °