Triangles Math Example 2

Follow the full solution, then compare it with the other examples linked below.

medium

Classify the triangle with sides

5

cm,

5

cm, and

8

cm by its sides and determine whether it is acute, right, or obtuse.

1
Since two sides are equal ( $5 = 5$ ), this is an isosceles triangle.
2
Check for right/obtuse: compare $c^2$ with $a^2 + b^2$ where $c = 8$ : $8^2 = 64$ vs $5^2 + 5^2 = 50$ .
3
Since $64 > 50$ , the triangle is obtuse (the angle opposite the longest side is greater than $90°$ ).

Answer

\text{Isosceles and obtuse}

Triangles can be classified by sides (scalene, isosceles, equilateral) and by angles (acute, right, obtuse). Comparing

c^2

a^2 + b^2

extends the Pythagorean theorem to classify any triangle.

About Triangles

A polygon with exactly three sides and three interior angles that always sum to exactly 180 degrees.

Two angles of a triangle measure [formula] and [formula]. Find the third angle.

An equilateral triangle has a perimeter of [formula] cm. Find the length of each side.

The three angles of a triangle are in the ratio [formula]. Find the measure of each angle.