a lamp post that is 8 feet high casts a shadow 5 feet long. how tall is the person standing beside the lamp post if his shadow is 3.5 feet long
When a 4-foot high stick is held perpendicular to the ground 12 feet away from a lamppost, it casts a 6-foot-high shadow. When the same stick is x feet away from the lamppost, it casts a 3 foot shadow. What is the value of x?
To find the height of the person standing beside the lamp post, you can set up a proportion using the given information.
Let's assume "x" as the height of the person.
The proportion would be:
Height of the lamp post / Length of the lamp post's shadow = Height of the person / Length of the person's shadow.
Plugging in the values we have:
8 feet / 5 feet = x / 3.5 feet.
Next, we can cross-multiply:
(8 feet)(3.5 feet) = (5 feet)(x).
28 feet = 5x.
Now, divide both sides of the equation by 5:
28 feet / 5 = 5x / 5.
5.6 feet = x.
Therefore, the person standing beside the lamp post is 5.6 feet tall.
To determine the height of the person standing beside the lamp post, we can use the concept of similar triangles. Similar triangles have corresponding angles that are equal, and their corresponding sides are proportional.
In this case, let's consider two similar triangles: the triangle formed by the lamp post, its shadow, and its height, and the triangle formed by the person, their shadow, and their height.
Given the measurements, we have:
For the lamp post:
Height (h): 8 feet
Shadow length (s): 5 feet
For the person:
Shadow length (s'): 3.5 feet
Using the ratios of corresponding sides of similar triangles, we can set up the following proportion:
(h / s) = (h' / s')
Replacing the values with known measurements, we get:
(8 / 5) = (h' / 3.5)
To solve for the height of the person (h'), we can cross-multiply and divide:
8 * 3.5 = 5 * h'
28 = 5h'
h' = 28 / 5
So, the height of the person standing beside the lamp post is approximately 5.6 feet.
the ratio of height to shadow length is the same, so
h/3.5 = 8/5
I imagine you can solve that for h.