Understanding the Properties and Measurements of Obtuse Triangles using the Law of Cosines

Obtuse Triangle

An obtuse triangle is a type of triangle where one of the angles is greater than 90 degrees

An obtuse triangle is a type of triangle where one of the angles is greater than 90 degrees. In other words, it is a triangle that has one angle that is “obtuse” or “larger” than a right angle. A right angle is exactly 90 degrees, so any angle greater than 90 degrees is considered obtuse.

In an obtuse triangle, the other two angles are acute angles, which means they are less than 90 degrees. The sum of all angles in any triangle is always 180 degrees, so in an obtuse triangle, the sum of the two acute angles will always be less than 90 degrees to make up for the larger obtuse angle.

There are different ways to classify an obtuse triangle based on the lengths of its sides. For example, an obtuse triangle can be scalene, meaning all three sides have different lengths, or it can be isosceles, meaning two sides have the same length. If all three sides have the same length, then the obtuse triangle is also equilateral.

In terms of properties, an obtuse triangle has a longer base than its height, as the longest side (known as the hypotenuse) is opposite the obtuse angle. The other two sides are shorter in comparison, and they are adjacent to the acute angles.

When working with an obtuse triangle, you can use the law of cosines to determine the lengths of its sides or the measure of its angles. The law of cosines states that in a triangle with sides of lengths a, b, and c, and an angle opposite side c, the following formula applies:

c^2 = a^2 + b^2 – 2abcos(C)

Where C is the measure of the angle opposite side c.

In summary, an obtuse triangle is a type of triangle that has one angle greater than 90 degrees, making it “obtuse.” It can have various side lengths, and its properties and measurements can be determined using the law of cosines.

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