Acute triangle

An acute triangle is a triangle with three acute angles, which are angles measuring less than 90°.

This yield sign is in the shape of an acute triangle.

Properties of acute triangles

Using the Pythagorean Theorem to find acute triangles

When the lengths of the sides of a triangle are known, the Pythagorean Theorem can be used to determine whether or not the triangle is an acute triangle.

For a right triangle with a hypotenuse of length c and leg lengths a and b, the Pythagorean Theorem states:

a2 + b2 = c2

On the other hand, in a triangle where a2 + b2 > c2, if side c is also the longest side, the triangle is an acute triangle.


Is triangle ABC an acute triangle?

Side AB above is the longest side of triangle ABC. To check if ABC is an acute triangle, let c = 13, a = 10 and b = 9:

a2 + b2 = 102 + 92 = 181

c2 = 132 = 169

181 > 169

Therefore triangle ABC is an acute triangle.