Question

At a certain time of the day, a shadow cast by susie and the shadow cash by a tree end at the same point. Susie is 6 feet and she is 30 feet from the base of the tree. The two shadows end at a point that is 40 feet from the base of the tree. Draw the scenario and find the height of the tree. The height of the tree is [a] feet.

Answer 1

You can use similar triangles to solve this problem. Here's a diagram to help illustrate the scenario:

A (top of Susie's shadow)
|\
| \
| \ (top of the tree's shadow)
| \
| \
| \
|------\
Susie Tree
(6 ft) (height = h)
Let's label the heights as follows:

Height of Susie (S) = 6 feet
Distance of Susie from the tree (a) = 30 feet
Height of the tree (h) = ?
Distance from the base of the tree to where the shadows meet (b) = 40 feet
We have two similar triangles:

The triangle formed by Susie's height, the distance of Susie from the tree, and the combined length of both shadows.
The triangle formed by the height of the tree, the distance of the tree's shadow, and the combined length of both shadows.
Using similar triangles, we can set up a proportion:

(Susie's height) / (Distance of Susie from the tree) = (Height of the tree) / (Distance from the base of the tree to where the shadows meet)

Plugging in the values:

(6 ft) / (30 ft) = (h) / (40 ft)

Now, solve for h:

h = (6/30) * 40
h = (1/5) * 40
h = 8 feet

So, the height of the tree is 8 feet.