Understanding the Hypotenuse: Definition, Properties, and Calculation using the Pythagorean Theorem

Hypotenuse

The hypotenuse is a term used in geometry and is specifically related to right triangles

The hypotenuse is a term used in geometry and is specifically related to right triangles.

In a right triangle, the hypotenuse is the side opposite the right angle, and it is the longest side of the triangle. The other two sides of the right triangle are called the legs.

The main property of the hypotenuse is that it is always the side that directly connects the two endpoints of the legs without any other side intersecting it. It is also the side that has the greatest length among all the sides of a right triangle.

The length of the hypotenuse can be determined using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.

Mathematically, the Pythagorean theorem can be expressed as:

c^2 = a^2 + b^2

Where c represents the length of the hypotenuse, and a and b represent the lengths of the legs. By rearranging the equation, we can solve for c:

c = √(a^2 + b^2)

For example, if the lengths of the legs are 3 units and 4 units, we can calculate the length of the hypotenuse as follows:

c = √(3^2 + 4^2)
= √(9 + 16)
= √25
= 5 units

Therefore, the length of the hypotenuse in this example is 5 units.

More Answers: