You are 6 feet in height. If you are standing away from the base of the lamppost, you can see where your shadow stops. If you are 10 feet from the base of the lamppost and your shadow stops 5 feet from where you stand, what is the height of the lamppost?
To determine the height of the lamppost, we can use similar triangles and the concept of proportions.
Here's how to solve it step-by-step:
Step 1: Draw a diagram to visualize the problem. Draw a vertical line to represent the lamppost, and a horizontal line to represent the ground. Mark a point for the base of the lamppost and another point to represent where you stand (10 feet away from the base). Label the height of the lamppost as "x" and your height as 6 feet.
Lamppost
----|
| |
| |<--- x
--|----|
|
|<--- You (6 feet)
Step 2: Notice that we have two similar triangles in this diagram - one formed by the lamppost, its shadow, and the distance from where you stand to the base, and the other formed by you, your shadow, and the same distance.
Step 3: Using the concept of similar triangles, we can set up the following proportion:
height of lamppost / length of its shadow = your height / length of your shadow
x / 5 = 6 / 10
Step 4: Cross-multiply the proportion:
6 * 5 = x * 10
30 = 10x
Step 5: Solve for x by dividing both sides of the equation by 10:
30 / 10 = x
3 = x
Therefore, the height of the lamppost is 3 feet.