Explain the Pythagorean theorem and provide an example where it is applied in geometry or real-world…

Question

Explain the Pythagorean theorem and provide an example where it is applied in geometry or real-world situations.

ScanSolve AI Tutor · Accepted Answer

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (legs). It is expressed by the formula: $a^2 + b^2 = c^2$ , where 'c' is the length of the hypotenuse, and 'a' and 'b' are the lengths of the other two sides.

Example:
Imagine you have a ladder that is 5 meters long, and you want to lean it against a wall. For safety, the base of the ladder must be 3 meters away from the wall. How high up the wall will the ladder reach?

Identify the right triangle
The ladder, the wall, and the ground form a right-angled triangle.
Assign variables
- The length of the ladder is the hypotenuse (c) = 5 meters.
- The distance from the wall to the base of the ladder is one leg (a) = 3 meters.
- The height the ladder reaches up the wall is the other leg (b), which we need to find.
Apply the formula
$a^2 + b^2 = c^2$
$3^2 + b^2 = 5^2$
$9 + b^2 = 25$
$b^2 = 25 - 9$
$b^2 = 16$
$b = \sqrt{16}$
$b = 4$ meters

So, the ladder will reach 4 meters high up the wall.

Explain the Pythagorean theorem and provide an example where it is applied in geometry or real-world situations.

Step-by-step solution

Identify the right triangle

Assign variables

Apply the formula

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