How tall is Big Ben? (Python Challenge)

In this blog post we will find an easy method to estimate the height of any high building or tree by measuring the length of its shadow in the ground. We will apply this method to estimate the height of Big Ben, London, UK; technically the Elizabeth Tower, Big Ben being the name of the large bell inside this clock tower. This challenge provides a practical application of similar triangles and basic trigonometry, which are fundamental concepts in geometry.

Similar Triangles Method

To estimate the height of a tree or a building using its shadow, we can use the concept of similar triangles. Here’s a simple diagram to illustrate the method:

The two triangles formed by both the Elizabeth Tower and its shadow and by the phone box and its shadow are similar triangles: two triangles are similar if the angles are the same size. As a consequence, the corresponding sides of these triangles are in the same ratio. We can therefore estimate the height of the clock tower using the following formula:

It’s effectively a lot more practical for anyone to measure the length of a shadow on the ground, and to measure the height of a smaller reference object such as a person or a telephone box, than to measure the actual height of a building!

Python Challenge

Your task is to write a Python program that will:

 Take three inputs: l, h, and L: The length of the telephone box shadow (l), the height of the telephone box (h) and the length of the shadow of the Elizabeth Tower (L)
 Use the three input values to work out the height of the Elizabeth Tower (H)
 Output the estimated height of the Elizabeth Tower to one decimal place.

To test your program use the following values:

Can you then use your program to estimate the height of the Eiffel Tower using a 1.85m tall French man as your reference object and the following shadow measurements:

Solution...

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