Relationships Between Angles and Sides of the Triangle

The basic relationship that exists between the sides and angles of a triangle is:

Opposite the longest side of the triangle is the angle largest in the triangle.

This relationship also holds true in reverse.

Opposite the longest side of the triangle is the largest angle of the triangle.

In the same way, we can say that:

Opposite the largest angle of the triangle is the longest side of the triangle.
And opposite the smallest angle of the triangle is the shortest side of the same.

In a right triangle

There is an angle of $90º$ degrees. We know that the sum of the angles of a triangle is $180º$ , therefore, the angle of $90º$ will be the largest in a right triangle.
We can determine that the hypotenuse, located opposite the right angle, is the longest side of a right triangle.
Similarly:

In an obtuse triangle

There is an angle that measures more than $90º$ . The side located opposite the obtuse angle is the longest of all.
In an isosceles triangle:
The sides are equal, therefore, the angles opposite the base sides are also equal.

We will be able to discover the real relationships between the sides and angles that, in fact, will help us find the values we need. We will study this in the chapter called Trigonometry, which deals with the relationships between the sides and angles of triangles.
Until then, simply remember the logic in the relationships between the sides and angles of triangles.

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