How to Tell If a Triangle Is Obtuse

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A triangle is a polygon with three sides, three vertices, and three angles. They are classified by their angles. Triangles can be obtuse, acute, or right triangles. In fact, all triangles will fit into one of these categories.

A right triangle has one angle with a measure of 90 degrees. If any triangle has this property, it is a right triangle. If it is a right triangle, it cannot be obtuse or acute. However, the other two angles will be acute. The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs. The hypotenuse will always be the longest side.

An acute triangle is one where each of the three angles is less than 90 degrees. An obtuse triangle will have one angle that is greater than 90 degrees, and this is the primary feature of this type of triangle. Any angle that is greater than 90 degrees is called an obtuse angle. Read on to learn how to tell if a triangle is obtuse.

Measure the Angles

If you want to classify a triangle, you need to know the measure of each angle. You cannot eyeball it because it is hard to determine the angle with the naked eye. However, you can use a protractor. Line the protractor edge up with one of the sides of the triangle, and follow the side next to it to see what it measures. If you find that it measures less than 90 degrees, you can move to the next angle. You will need to measure all three to find out if one of the angles is obtuse. It only takes one obtuse angle to have an obtuse triangle.

You should double check your measurements by making sure that the three angles add up to 180 degrees. Another triangle rule is that the three angles will always add up to 180 degrees. If one of the angles is greater than 90 degrees, you have an obtuse triangle.

Use the Three Side Lengths to Find Out

If you know the three side lengths, you can use the Pythagorean Theorem to find out if the triangle is obtuse. The Pythagorean theorem for right triangles says the a squared plus b squared equals c squared. However, if a squared plus b squared is greater than c squared, then the triangle is acute. On the other hand, if a squared plus b squared is less than c squared, the triangle will have an obtuse angle and be obtuse.

For example, if you have a triangle with side lengths of 4, 10, and 15, you can plug these lengths into the equation. Four squared is 16, ten squared is 100, and 15 squared is 225. From this, we get the equation 16 + 100 = 116, and since 116 is less than 225, you have an obtuse triangle.

Does the Triangle Have One Significantly Larger Angle?

When you are looking at a triangle, if one angle is clearly larger than 90 degrees, then you have an obtuse triangle. If the angle is close to 90 degrees, you will have to measure it to be sure, but if it is clearly greater than 90 degrees, you can safely call it an obtuse triangle.

Obtuse triangles have one angle that is greater than 90 degrees. Because all three angles cannot be more than 180 degrees, the other two angles must be obtuse. The most accurate way to determine whether you have an obtuse triangle is to measure the angles. You can also use the Pythagorean theorem to make sure that the square of two sides added together is less than the square of the side opposite the obtuse angle.

An equilateral triangle is one where all three sides have the same length, and this kind of triangle must be acute. Each angle will be 60 degrees, which means that none are greater than 90 degrees. An obtuse triangle can be an isosceles triangle, where two sides have equal lengths. It can also be scalene, where all three sides are different lengths. Once you become familiar with the properties of obtuse, acute, and right triangles, it is not too hard to classify a triangle.

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