You place a mirror on the ground 6 feet from the lamppost. you move back 3 feet and see the top of the lamppost in the mirror. What is the height of the lamppost?
Depending on your height if i am 5ft then it is 10ft
You have to set up a proportion, then you have to multiply it by 2
To find the height of the lamppost, we can use similar triangles. Here's how:
1. Draw a diagram: Sketch a right-angled triangle representing the situation. The lamppost is represented by a vertical line, the distance from the lamppost to the mirror is the base of the triangle, and the height of the lamppost is the height of the triangle.
|
|
|‾‾‾‾‾‾‾\
| \
| \ Height of lamppost
| \
| \
|‾‾‾‾‾‾‾‾‾\
Base (distance from lamppost to mirror)
2. Determine the similar triangles: Notice that the small triangle formed by the line from the top of the lamppost to the mirror, the line from the top of the lamppost to your position, and the line from your position to the mirror is similar to the larger triangle we drew.
3. Set up the proportion: Since the triangles are similar, we can set up a proportion using their corresponding sides. Let's call the height of the lamppost "h" and the distance you moved back "d". The distance from the lamppost to the mirror is given as 6 feet.
(h / d) = (Height of the small triangle / 6)
4. Substitute the values: We know that the height of the small triangle is 3 feet (given in the question) and the distance you moved back is 3 feet (given in the question).
(h / 3) = (3 / 6)
5. Solve for "h": Cross-multiply and solve for "h".
6h = 9
h = 9 / 6 = 1.5 feet
Therefore, the height of the lamppost is approximately 1.5 feet.