Verify experimentally that the angle opposite to the longer side is greater than the angle opposite to the shorter side in any triangle (at least two figures are
necessary)

If two sides of a triangle are unequal, the angle opposite to the longer side is larger (or greater). You may prove this theorem by taking a point P on BC such that CA = CP.

Step-by-step explanation:

That's how you can prove which side is bigger

Given:

The figure of a triangle.

The perimeter of the triangle ABC is 31.

To find:

The value of x in the given triangle.

Solution:

Three sides of the triangle ABC are AB, BC, AC are their measures are respectively.

The perimeter of the triangle ABC is 31.

Subtract 7 from both sides.

Now, the measures of the sides are:

And,

Using the law of cosines, we get

Using calculator, we get

Therefore, the value of x is 37.0 degrees.