Importance of the Pythagoras’ theorem in our daily life

Importance of the Pythagoras' theorem in our daily life

Pythagoras is a name of a Greek mathematician, who proved the relationship between the sides of a right-angled triangle. The importance of Pythagoras' theorem in our daily life can be seen in the following examples:

(a) Shortening travelling distance

The Pythagoras' theorem helps to shorten the route from one place to another. For example, Figure 1 shows a standard seven pupil who lives in street A and studies at a school located in street C. The pupil can use two ways to reach the school. The pupil can use the road from street A via street B. Also, the pupil can go straight to school by using the road from street A to street C.

(b) Drawing plans of different buildings

Architects use the Pythagoras' theorem to draw architectural plans of different buildings and other construction works. Such plans include houses, schools, hospitals, industries, airports, roads and bridges.

(c) Drawing maps of different cities

Architects use the Pythagoras' theorem to find the distance and height of different objects when drawing maps of cities. For instance, finding the slope of hills and mountains.

(d) Construction of the foundation of a building with two walls forming a right-angled corner between them

Masons use the Pythagoras' theorem to construct a house foundation whose two walls meet and form a right angle. For instance, the lengths of the three sides of right-angled triangle are 3 metres by 4 metres by 5 metres. These are used by masons to measure the foundation with right-angled walls by using a rope that makes the length of the walls.

Recognising the sides of the right-angled triangle

A right-angled triangle has three sides: the base, height and hypotenuse. One of the three angles of the triangle, is a right angle (90 degrees). The right angle is formed by two sides which are the base and height. In Figure 6, the horizontal side of the right-angled triangle is called the base and the vertical side is called the height. The opposite side of the right angle is called the hypotenuse. The hypotenuse is the longest side of all sides. However, the hypotenuse is shorter than the total length of the base and height.

Triangle ABC in Figure 7 is the right-angled triangle. Angle ACB is a right angle, that is ∠ACB = 90°.

BA is the longest side of all sides which is called the hypotenuse and its length is c. CA is the height whose length is b. CB is the base whose length is a.

Therefore, the lengths of the right-angled triangle ABC are a, b, and c. The following are examples of right-angled triangles with the base, height, and hypotenuse.