If Dave is 6 feet tall and casts a shadow of 15 feet, what is the height of a tree that casts a shadow of 81 feet? Draw a diagram and solve for the height of the tree.
6/15 = x/81
To solve this problem, we can use proportions and set up a ratio between the height of Dave and the length of his shadow, and then use the same ratio to find the height of the tree.
Let's draw a diagram to help visualize the situation:
```
|\
| \
Dave | \ Tree
-------|---\
| \
| \
6ft | \ Unknown height (H)
| \
|________\
15ft 81ft
```
In this diagram, we have Dave, whose height is 6 feet, casting a shadow of 15 feet. On the other hand, there is a tree casting a shadow of 81 feet, and we need to calculate its height (H).
Using proportions, we can set up the following equation:
Dave's height / Dave's shadow = Tree's height / Tree's shadow
Simplifying this equation, we get:
6ft / 15ft = H / 81ft
To find the value of H, we can cross-multiply:
6ft * 81ft = 15ft * H
486ft = 15ft * H
Now, we can solve for H by dividing both sides of the equation by 15ft:
H = 486ft / 15ft
H ≈ 32.4ft
Therefore, the height of the tree is approximately 32.4 feet.