Regarding side length, a triangle is an obtuse triangle if …
A triangle is considered an obtuse triangle if one of its angles measures greater than 90 degrees
A triangle is considered an obtuse triangle if one of its angles measures greater than 90 degrees. In terms of side lengths, we can determine if a triangle is obtuse by using the Pythagorean Theorem and comparing the squares of the lengths of the three sides.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem can also be applied to determine if a triangle is obtuse.
Let’s denote the three sides of a triangle as a, b, and c. To determine if the triangle is obtuse, we must consider the relationship between the squares of these side lengths.
If the square of the longest side (c²) is greater than the sum of the squares of the other two sides (a² + b²), then the triangle is obtuse. Mathematically, the condition for an obtuse triangle can be expressed as:
c² > a² + b²
For example, let’s consider a triangle with side lengths a = 5 units, b = 12 units, and c = 13 units. We can determine if it is obtuse by evaluating the equation:
13² > 5² + 12²
169 > 25 + 144
169 > 169
Since the inequality is true, we can conclude that this triangle is obtuse.
It’s essential to note that the condition for an obtuse triangle relies on the longest side being opposite to the angle greater than 90 degrees.
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