Triangle ABC is classified as an acute triangle because all its angles are acute and the sum of its angles is 180 degrees.
The triangle ABC is classified as an acute triangle. An acute triangle is a triangle that has all its angles less than 90 degrees. In this case, angle ABD and angle ADB are both 60 degrees, which means they are acute angles. Angle A is also 60 degrees, so it is an acute angle as well.
To further confirm that triangle ABC is an acute triangle, we can calculate the sum of its angles. Angle BDC is 120 degrees, and angles BCD and DBC are both 30 degrees. The sum of all these angles is 120 + 30 + 30 = 180 degrees, which is equal to the sum of angles in a triangle.
In conclusion, triangle ABC is an acute triangle because all its angles are acute and the sum of its angles is 180 degrees.