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?

Question

Eli Assouline · Accepted Answer

The height of the tree is #18.67# feet

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? #2/1.5 = x/14" "larr# cross multiply #x = (2xx14)/1.5# #x = 18.67# feet

Abigail Allen · Answer

undefined To find the height of the tree, we can use similar triangles.

Let $ h $ be the height of the tree.

Using the similar triangles formed by the tree, its shadow, the pole, and its shadow:

$$
\frac{{\text{{Height of tree}}}}{{\text{{Length of tree's shadow}}}} = \frac{{\text{{Height of pole}}}}{{\text{{Length of pole's shadow}}}}
$$

$$
\frac{h}{14} = \frac{2}{1.5}
$$

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

$$
h \approx 18.67 \text{ feet}
$$

So, approximately, the height of the tree is 18.67 feet.