Question

A 1.6-m - tall women stands next to the Eiffel Tower. At this time of the day, her shadow is 0.5 m long. At the same time, the tower’s shadow is 93.75 m long. How tall is the Eiffel Tower?

Answer 1

We can graph the situation as follows:

Since the shadow must have the same angle, we can use the tangent of this angle to find the height of the tower.

Then, we have that:

`\tan (\alpha)=(1.6)/(0.5)\Rightarrow\tan (\alpha)=3.2\Rightarrow arctan(\tan (\alpha))=\arctan (3.2)`

Then

`\alpha=\arctan (3.2)\Rightarrow\alpha=72.64`

Thus, we can use this angle to find the height of the Eiffel Tower:

`\tan (72.64)=(h)/(93.75)\Rightarrow h=93.75\cdot3.2\Rightarrow h=300`

Then, the height of the Eiffel Tower, according to this, is 300 m.