The dihedral angle is 120 ° degrees. Inside it, point A is given, which is located at a distance of 24 cm from both edges of the corner. What is the distance from point A to the edge of the dihedral angle?
From point A, construct perpendiculars AB and AC to the faces of the dihedral angle.
Then the angle ABO = ASO = 90, and therefore the triangles AOB and AOC are rectangular.
By condition, the lengths of the segments AB = AC = 24 cm.
Then, in the right-angled triangles AOB and AOS, the hypotenuse of AO is common, and the legs AB and AC are equal to each other, which means that the right-angled triangles AOB and AOC are equal in leg and hypotenuse, the fourth sign of equality of right-angled triangles.
Then the angle AOB = AOC = BOC / 2 = 120/2 = 600.
In a right-angled triangle AOB, Sin AOB = AB / AO.
AO = AB / Sin AOB = 24 / Sin60 = 24 / (√3 / 2) = 48 / √3 = 16 * √3 cm.
Answer: From point A to the edge of the dihedral angle 16 * √3 cm.
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