Thales Theorem Application

Application of the Thales Theorem

We're using:

• What we want to measure

• A pen

• And a ruler

First we measure the pen and write down its height to use it later. In my case, this pen is 13.4 cm long.

We place the objects, one next to the other, against a light so that we can see its shadow without difficulty.

Now we measure the shadow of the pen and that of the object we want to measure.

In my case the shadow of the pen is 18 cm long and the shadow of the other object is 21 cm long.

Now it´s time to use the formula.

Thales' theorem tells us that, if the two triangles that make up these objects are proportional, then dividing the height of the pen by its shadow gives us the same thing as dividing the height of the other object by its shadow.

Knowing this, we only need to do the calculation and we will obtain the height of the object to be measured as a result.

13,4 / 18 = (Object's Height) / 21

In this case we do not know the height of the second object, so to calculate it we must replace it by moving the values from one side to the other.

15,6 = (Object's Height)

13,4 · 21 / 18 = (Object's Height)