There are six types or classifications of triangles, and every triangle will fit into two classifications based on the angles of the triangle and the lengths of the triangle's sides.
We start by determining what type a 120 30 30 triangle is based on its angles. It will be an Acute Triangle, Obtuse Triangle, or Right Triangle.
Acute Triangle
Is a 120 30 30 triangle an acute triangle? A triangle is an acute triangle if all three angles are less than 90 degrees. All three angles in a 120 30 30 triangle are not less than 90 degrees. Therefore, a 120° 30° 30° triangle is not an acute triangle.
Obtuse Triangle
Is a 120 30 30 triangle an obtuse triangle? A triangle is an obtuse triangle if one of the angles is greater than 90 degrees. One of the angles in a 120 30 30 triangle is greater than 90 degrees. Therefore, a 120° 30° 30° triangle is an obtuse triangle.
Right Triangle
Is a 120 30 30 triangle a right triangle? A triangle is a right triangle if one of the angles is 90 degrees. None of the angles in a 120 30 30 triangle is 90 degrees. Therefore, a 120° 30° 30° triangle is not a right triangle.
Next we will determine what type a 120 30 30 triangle is based on the length of the sides of the triangle. If we set the length AB on a 120 30 30 triangle to 100, then we can calculate the length BC and the length AC as follows:
AB = 100
BC = AB × sin(A deg) ÷ sin(C deg)
BC = 100 × sin(120 deg) ÷ sin(30 deg)
BC ≈ 173.205
AC = AB × sin(B deg) ÷ sin(C deg)
AC = 100 × sin(30 deg) ÷ sin(30 deg)
AC = 100
Now we have the information needed to determine if a 120 30 30 triangle is an Isosceles Triangle, Equilateral Triangle, or Scalene Triangle.
Isosceles Triangle
Is a 120 30 30 triangle an isosceles triangle? A triangle is an isosceles triangle if exactly two of the sides have the same length. That is the case here. Therefore, a 120° 30° 30° triangle is an isosceles triangle.
Equilateral Triangle
Is a 120 30 30 triangle an equilateral triangle? A triangle is an equilateral triangle if all three sides have the same length. All three sides in a 120 30 30 triangle are not the same length. Therefore, a 120° 30° 30° triangle is not an equilateral triangle.
Scalene Triangle
Is a 120 30 30 triangle a scalene triangle? A triangle is a scalene triangle if all the sides are different. All the sides of 120 30 30 triangle are not different. Therefore, a 120° 30° 30° triangle is not a scalene triangle.
In summary, based on the information above, the answer to "What type is a 120 30 30 triangle?" is as follows:
Obtuse Isosceles Triangle
What Type of Triangle?
Here you can determine the type of another triangle by entering its angles.
What type is a 120 31 29 triangle?
What type is the next triangle on our list? Find out here!