In a right angled triangle, the square of the hypotenuse side of the triangle is equal to the sum of the opposite side and adjacent sides of the triangle (Eves, 1997). This is known as the Pythagoras triangle. There are various applications of Pythagoras theorem in day-to-day situation that involves right angled triangles. An example of the application of Pythagoras theorem involving right angle triangles in day-to-day situations is in the determination of the height of a window from the foot of the ground.
It is quite difficult to accurately determine the height of a window from the foot of the ground, but with the application of Pythagoras theorem this makes it easier. Assuming, we have a rigid ladder that leans against a vertical house, touching the window whose height is to be determined. This forms a right angled triangle. The distance from the base of the ladder to the foot of the building represents the adjacent side of the triangle and the length of the ladder is the hypotenuse side of the triangle, the height of the window whose length is to be determined is the opposite side of the triangle.
Let the length of the ladder be represented by h, the distance between the foot of the ladder and the foot of the building be represented by a, then the height of the window from the base of the building be represented by o. Each parameter represents the hypotenuse, adjacent and the opposite sides of the triangle. Mathematically, applying Pythagoras theorem, h2= o2 + a2 The length of the window is the opposite side of the triangle and is represented by o above. Therefore making o the subject of the formulae,
We have o= v (h2 – a2). So given that we know the length of the ladder and the horizontal distance between the foot of the ladder and the foot of the building, then the height of the window can be calculated using the above formulae. The application of Pythagoras theorem in the determination of the height of a window further validates the authenticity of the theorem.
Eves, H. (1997). Foundations and Fundamental Concepts of Mathematics. New York: Dover Publications.