A 60 foot light pole casts a shadow that is 40 feet long. At the same time, a nearby light post casts a shadow that is 15 feet long. How tall is the light post?
Use a proportion. Cross multiply and solve for x.
60/40 = x/15
Well, let's take a look at these poles. It appears that one pole has a shadow that is 40 feet long, while the other pole's shadow is only 15 feet long. Quite a difference, I must say.
Now, if we use a little bit of math and assume that the length of the first pole is x, we can set up a proportion:
60 feet (length of the shadow for the first pole) / 40 feet (length of the actual pole) = 15 feet (length of the shadow for the second pole) / x (length of the second pole).
Solving for x, we get x = (15 feet * 40 feet) / 60 feet, which equals... drumroll, please... 10 feet!
So, the height of the nearby light post is 10 feet. Just remember, not everything is as tall as it may seem. Keep those shadows in check!
To find out the height of the light post, we can set up a proportion using the lengths of the shadows.
Let's call the height of the light post "h".
The proportion will be:
height of the light post / length of its shadow = height of the 60 foot light pole / length of its shadow
h / 15 = 60 / 40
To solve for h, we can cross multiply:
40h = 60 x 15
40h = 900
Now, divide both sides by 40:
h = 900 / 40
Hence, the height of the light post is 22.5 feet.
To find the height of the light post, you can use the concept of similar triangles.
Let's consider the ratio of the height of the light pole to the length of its shadow. This ratio will be the same as the ratio of the height of the nearby light post to the length of its shadow.
For the first light pole:
Height of light pole / Length of shadow = 60 feet / 40 feet
For the nearby light post:
Height of nearby light post / Length of shadow = ?
Since we know these two ratios are equal, we can set up the following equation:
60 feet / 40 feet = Height of nearby light post / 15 feet
Now, we can solve for the height of the nearby light post. We can cross-multiply and then divide to find the height:
(60 feet * 15 feet) / 40 feet = Height of nearby light post
900 feet * feet / 40 feet = Height of nearby light post
⇒ (900 feet / 40 feet) * feet = Height of nearby light post
⇒ 22.5 feet * feet = Height of nearby light post
Therefore, the height of the nearby light post is 22.5 feet.