Transformations and SymmetrySimilar Triangles

Here you can see the image of a large lighthouse. Together with a friend, you want to measure the height of the lighthouse, but unfortunately we cannot climb to the top.

It turns out that, very well hidden, the diagram contains two similar triangles: one is formed by the lighthouse and its shadow, and one is formed by your friend and her shadow.

Both triangles have one right angle at the bottom. The sun rays are parallel, which means that the other two angles at the bottom are corresponding angles, and also equal. By the AA condition for triangles, these two must be similar.

We can easily measure the length of the shadows, and we also know the height of your friend. Now we can use the proportionality of sides in similar triangles to find the height of the lighthouse:

COMING SOON – Equation

Therefore the lighthouse is 1.5m tall.