What type is a 45 45 90 triangle?

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 45 45 90 triangle is based on its angles. It will be an Acute Triangle, Obtuse Triangle, or Right Triangle.

Acute Triangle
Is a 45 45 90 triangle an acute triangle? A triangle is an acute triangle if all three angles are less than 90 degrees. All three angles in a 45 45 90 triangle are not less than 90 degrees. Therefore, a 45° 45° 90° triangle is not an acute triangle.

Obtuse Triangle
Is a 45 45 90 triangle an obtuse triangle? A triangle is an obtuse triangle if one of the angles is greater than 90 degrees. None of the angles in a 45 45 90 triangle is greater than 90 degrees. Therefore, a 45° 45° 90° triangle is not an obtuse triangle.

Right Triangle
Is a 45 45 90 triangle a right triangle? A triangle is a right triangle if one of the angles is 90 degrees. One of the angles in a 45 45 90 triangle is 90 degrees. Therefore, a 45° 45° 90° triangle is a right triangle.

Next we will determine what type a 45 45 90 triangle is based on the length of the sides of the triangle. If we set the length AB on a 45 45 90 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(45 deg) ÷ sin(90 deg)
BC ≈ 70.711

AC = AB × sin(B deg) ÷ sin(C deg)
AC = 100 × sin(45 deg) ÷ sin(90 deg)
AC ≈ 70.711

Now we have the information needed to determine if a 45 45 90 triangle is an Isosceles Triangle, Equilateral Triangle, or Scalene Triangle.

Isosceles Triangle
Is a 45 45 90 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 45° 45° 90° triangle is an isosceles triangle.

Equilateral Triangle
Is a 45 45 90 triangle an equilateral triangle? A triangle is an equilateral triangle if all three sides have the same length. All three sides in a 45 45 90 triangle are not the same length. Therefore, a 45° 45° 90° triangle is not an equilateral triangle.

Scalene Triangle
Is a 45 45 90 triangle a scalene triangle? A triangle is a scalene triangle if all the sides are different. All the sides of 45 45 90 triangle are not different. Therefore, a 45° 45° 90° triangle is not a scalene triangle.

In summary, based on the information above, the answer to "What type is a 45 45 90 triangle?" is as follows:

Right Isosceles Triangle

What Type of Triangle?
Here you can determine the type of another triangle by entering its angles.

∠A = °

∠B = °

∠C = °

What type is a 45 46 89 triangle?
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