▷5 Examples of the Pythagorean theorem Explained!🥇

What is the Pythagorean theorem?

He Pythagoras theorem List the 3 sides of a right triangle and mention the following:

The square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

Look at the Pythagorean theorem in the graph below.

From image:

Legs: a, b (with the sides that form the right angle) Hypotenuse: c (it is the longest side of the right triangle, it is also identified as the opposite side of the right angle)

Then it is fulfilled:

c² = a² + b²

This pythagoras formula is perhaps the most famous of all time and is generally used to find one side of a right triangle, given two of them.

The following video explains what the Pythagorean theorem is with examples.

Next, we will see various applications of the Pythagorean theorem.

Examples of the Pythagorean theorem

Example 1:

In the following graph, calculate the value of the hypotenuse.

Solution:

Let the hypotenuse be: “x”

Since we are asked for the hypotenuse, we apply the studied theorem:

x² = 5² + 12²

⇒ x² = 25 + 144 = 169

Solving:

∴ x = 13cm

Example 2:

In the following figure calculate the value of x

Solution:

In the figure we see that “x” is a leg, we know the other 2 sides, so we apply the Pythagorean theorem:

5² = x² + 3²

Ordering and solving:

x² = 25 – 9 = 16

⇒ x = 4u

The triangle with sides 3, 4, and 5 is a Pythagorean right triangle.

Example 3:

In the figure below, find the value of x.

In this figure the value of x is on all 3 sides, so we quickly apply the Pythagorean theorem:

Solving and factoring we have:

(x -17)(x – 5) = 0

From here it can be said that:

x = 17

Example 4:

Calculate the height of the building in the following figure.

Solution:

To calculate the height of the building, we must make a “important stroke”, observe:

AP is drawn in such a way that:

ΔAPC = Isosceles Triangle

⇒ AP = 50cm

Therefore, in the right triangle ABP we apply the Pythagorean theorem:

AP² = AB² + BP²

Substituting and solving,

50² = h² + 30²

⇒ h = 40m

The height of the building is 40m.

Example 5:

In the following graph, T is the midpoint of AO and P is the point of tangency. Calculate AP.

Solution:

Since P is a point of tangency, we take the opportunity to draw OP and apply the property of the circumference:

OP ⊥ AB

Be:

AP = x = ??

Let’s see in the graph:

In addition, we see that the right triangle APO is formed, in which ordering the data, we apply the Pythagorean theorem, like this:

AO² = PA² + PO²

Replacing:

4² = x² + 2²

Finally, we give you more examples of the Pythagorean theorem in the following video. Enjoy it!