Is Pythagoras theorem actually useful?

The Pythagoras Theorem is a fundamental concept in mathematics that states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. While it may seem abstract, the Pythagoras Theorem has a wide range of real-life applications. Here are some examples:

1. Construction and architecture: Builders and architects use the Pythagoras Theorem to ensure that buildings are square and to calculate the length of diagonal walls. For example, if a wall is 6 feet high and 8 feet wide, the Pythagorean Theorem can be used to calculate the length of the diagonal:

c² = a² + b²

c² = 6² + 8²

c² = 36 + 64

c² = 100

c = 10 feet

So the length of the diagonal is 10 feet.

2. Navigation: The Pythagoras Theorem is used in navigation to calculate distances between points on a map. For example, if you want to find the distance between two points on a map that are 10 miles apart horizontally and 8 miles apart vertically, you can use the Pythagoras Theorem to calculate the straight-line distance between them:

c² = a² + b²

c² = 10² + 8²

c² = 100 + 64

c² = 164

c ≈ 12.81 miles

So the straight-line distance between the two points is approximately 12.81 miles.

3. Sports: The Pythagoras Theorem is used in sports to calculate the distance a ball has travelled or the angle it needs to be kicked or thrown to reach a target. For example, in football, a quarterback can use the Pythagoras Theorem to calculate the straight-line distance to a receiver and adjust their throw accordingly.

4. Surveying and land measurement: The Pythagoras Theorem is used in surveying and land measurement to calculate distances and angles between points. For example, if you want to calculate the distance between two points on a land survey map that are 150 feet apart horizontally and 100 feet apart vertically, you can use the Pythagoras Theorem to calculate the straight-line distance between them: c² = a² + b² c² = 150² + 100² c² = 22,500 + 10,000 c² = 32,500 c ≈ 180.28 feet So the straight-line distance between the two points is approximately 180.28 feet.

5. Medical imaging: The Pythagoras Theorem is used in medical imaging to calculate the length of the diagonal of a CT or MRI scan. For example, if a CT scan shows a tumour that is 3 cm high and 4 cm wide, the Pythagoras Theorem can be used to calculate the length of the diagonal of the tumour: c² = a² + b² c² = 3² + 4² c² = 9 + 16 c² = 25 c = 5 cm So the length of the diagonal of the tumour is 5 cm.

These are just a few examples of the many real-life applications of the Pythagoras Theorem. Its usefulness is not limited to these fields, and it has been used in many other areas, including physics, engineering, and even medicine. The Pythagoras Theorem is a testament to the power of mathematics and its ability to solve practical problems in the real world.

Written by: Parigya Mittal