Question

a stop sign casts a shadow that is 4 feet long at the same time that a tree casts a shadow that is 36 feet long. If the stop sign is 7 feet tall, how tall is the tree

Answer 1

You can use similar triangles to find the height of the tree. The ratio of corresponding sides in similar triangles is equal. Let \( h_s \) be the height of the stop sign, \( s_s \) be the length of the stop sign's shadow, \( h_t \) be the height of the tree, and \( s_t \) be the length of the tree's shadow.

The ratio is given by:

\[ \frac{h_s}{s_s} = \frac{h_t}{s_t} \]

Substitute the given values:

\[ \frac{7}{4} = \frac{h_t}{36} \]

Now, solve for \( h_t \):

\[ h_t = \frac{7}{4} \times 36 \]