A person is 7 ft tall and his shadow is 10 ft tall. using the same info what is the shadow of a person who is 5ft tall

Thanks Debra

 

Hi Debra.

Think of two people, one who is 7 ft tall and the other who is 5 ft tall, standing side by side like the diagram on the right.

If we draw their heights, shadows and the sun lines (the shadow lines connecting the tops of their heads to the tops of their shadows' heads), we get the diagram below:

shadows
triangles

As you can see, the sun lines (the diagonals) are parallel and of course so are the vertical and horizontal sides. These are similar triangles.

One of the most important property of similar triangles is that the ratios of their corresponding sides is always the same.

 
This means that   Tall Height   =   Tall Shadow Length
Short Height Short Shadow Length