Obtuse Triangle
A triangle with one angle that is greater than 90 degrees.
An obtuse triangle is a triangle that has one angle measuring greater than 90 degrees. The other two angles in an obtuse triangle measure less than 90 degrees.
In an obtuse triangle, the side opposite the obtuse angle is the longest side since the angle formed by this side is the largest angle. The other two sides of the triangle are shorter than the longest side.
To determine if a triangle is obtuse, you can measure each angle using a protractor or use the Pythagorean theorem if the lengths of the sides are given. If the sum of the squares of the two shorter sides is less than the square of the longest side, then the triangle is obtuse.
Obtuse triangles have some unique geometric properties such as their altitudes lie outside the triangle and their circumcenter lies outside the triangle. The circumcenter is the center of the circle that passes through all the vertices of the triangle.
Knowing that a triangle is obtuse can help you when trying to solve problems involving the triangle. For example, if you are asked to find the area of an obtuse triangle, you can use the formula for the area of a triangle (one-half base times height) and use the altitude drawn from the vertex opposite the obtuse angle.
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