First application:

We are now  ready to calculate the height of a tree, building, statue, ...

Example:

We can assume that a tree and a person (or our 1m stick) are standing perpendicular to the ground. We can draw two triangles, made by the tree or person, the shadow on the ground and a line from the top of the tree to the end of the shadow. We notice that both triangles are equiangular (similar angles), or we have two simular triangles. If two triangles are simular, then their sides are proportional, in order!

We can label the unknown height of the tree as x:

Now it's up to you, try these English, Spanish, Dutch and French exercises:

1) A building casts a shadow of lenght 2.1 m. At the same time, a 1m high pole casts a shadow of length 0,75m. How tall is the building?

2)

 

3)

more Spanish exercises: See the French answers

          

Spanish students at work with European exercises

Exercice 1 A quelle distance de la Tour Eiffel cette photo a-telle été prise?

 

Exercice 2

Zlatana souhaite déterminer la hauteur du collège. Elle se place de telle sorte que son ombre coïncide avec celle du collège. Une camarade  effectue alors les mesures suivantes (la figure n’est évidemment pas à l’échelle). Déterminer la hauteur du collège.

 

 

 

 

 

 

 

Exercice 3