To classify a triangle as acute, obtuse, or right, you can use the Pythagorean Theorem and its related inequality rules.
Understanding Triangle Classification:
Acute Triangle: All angles are less than 90 degrees.
Obtuse Triangle: One angle is greater than 90 degrees.
Right Triangle: One angle is exactly 90 degrees.
Using the Pythagorean Inequality:
Let's identify the longest side, which is often the "hypotenuse" in right triangles or acts as the potential indicator of an obtuse triangle.
Given sides of 10 cm, 24 cm, and 33 cm, the longest side is 33 cm.
To determine if this is a right, obtuse, or acute triangle, apply the Pythagorean Theorem to check:
Right Triangle:
�
2
=
�
2
+
�
2
c
2
=a
2
+b
2
, where
�
c is the longest side.
Acute Triangle:
�
2
<
�
2
+
�
2
c
2
<a
2
+b
2
.
Obtuse Triangle:
�
2
>
�
2
+
�
2
c
2
>a
2
+b
2
.
Calculate the Squares of the Sides:
1
0
2
=
100
10
2
=100,
2
4
2
=
576
24
2
=576,
3
3
2
=
1089
33
2
=1089.
Check the Pythagorean Inequality:
Calculate
�
2
+
�
2
a
2
+b
2
:
100
+
576
=
676
100+576=676.
Compare
�
2
c
2
with
�
2
+
�
2
a
2
+b
2
:
1089
>
676
1089>676.
