# A tree casts a shadow that is 14 feet long at the same time that a nearby 2-foot-tall pole casts a shadow that is 1.5 feet long Approximately how tall is the tree?

Dec 19, 2016

The height of the tree is $18.67$ feet

#### Explanation:

The pole and the tree both cast shadows. The triangles which form are similar triangles, because the sun is shining from the same angle in the sky.

You can write this as a direct proportion. (height : shadow)

2 is to 1.5 as what is to 14?

$\frac{2}{1.5} = \frac{x}{14} \text{ } \leftarrow$ cross multiply

$x = \frac{2 \times 14}{1.5}$

$x = 18.67$ feet