How to Calculate the Height of a Pole Using the Pythagorean Theorem

Question:

If the supporting wire to the top of a vertical pole is 13m long and is fastened to the ground at a point 5m away from the foot of the pole, how high is the pole?

Answer:

The height of the pole can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. Given the information provided, the pole is 12m high.

The problem can be solved by applying the Pythagorean theorem, a fundamental concept in geometry. The theorem is used to calculate the missing side or hypotenuse of a right triangle based on the lengths of the other two sides.

In this case, we have a right triangle formed by the supporting wire (hypotenuse), the distance from the foot of the pole to the point where the wire is fastened (one side), and the height of the pole (the other side).

Given that the wire is 13m long and the distance to the fixed point is 5m, we can set up the equation:

13² = h² + 5²

Where h represents the height of the pole. By simplifying the equation, we get:

169 = h² + 25

Subtracting 25 from both sides gives us h² = 144. Taking the square root of 144, we find that the pole is 12m high.

Understanding the Pythagorean theorem is crucial in solving various geometric problems involving right triangles. It provides a method to calculate unknown sides or angles, making it a valuable tool in mathematics and real-world applications.