A street sign casts a 12-foot 9-foot shadow. The lamppost next to it cast a 24-foot shadow. How tall is the lamppost?

Answer 1

Theodore Abad

The lamp post is #color(green)32'# tall.

12' street sign casts a shadow of 9'.

To find the height of the lamp post, with its shadow 24'

Since both the shadows are 9 : 24, the heights will be in x : 12, where x is the height of the lamp post.

# x / 12 = 24 / 9#

#x = (24 * 12) / 9#

#x = ((8 * cancel3) * (4 * cancel3)) / cancel9 = 32'#

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Answer 2

Caroline Aucoin

To find the height of the lamppost, we can use similar triangles. Since the street sign and the lamppost are both upright objects, the height of the lamppost can be determined by setting up a proportion using the lengths of their shadows and their respective heights.

Let x be the height of the lamppost.

Then, we have the proportion:

x/24 = 12/9

Solving for x:

x = (24 * 12) / 9

x = 32

So, the height of the lamppost is 32 feet.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.