A person 69 inches tall stands 40 feet from the base of a streetlight. the street light casts a shadow of length 96 inches how far above the ground is the streetlight

In order to determine how far above the ground a streetlight is, we will need to use a bit of trigonometry. Specifically, we will use the concept of similar triangles to find the height of the streetlight.

Let's start with the information we have: a person who is 69 inches tall stands 40 feet (480 inches) from the base of the streetlight. We also know that the streetlight casts a shadow of length 96 inches.

First, we need to create a diagram to help us visualize the problem. Here is what our diagram might look like:

               |
               |
            S  |   L
               |  
               |    
               |    
               |      
               |h    
_______________|______
       D        P      Q

In this diagram, S represents the top of the streetlight, L represents the base of the streetlight, P represents the top of the person's head, Q represents the bottom of the person's feet, D represents the end of the person's shadow, and h represents the height of the streetlight.

We know that the person is 69 inches tall, so the distance from P to Q is 69 inches. We also know that the person's shadow is 96 inches long, so the distance from Q to D is 96 inches. Finally, we know that the person is standing 40 feet (480 inches) from the base of the streetlight, so the distance from Q to L is 480 inches.

Now we can use similar triangles to find the height of the streetlight. Similar triangles are triangles that have the same shape but different sizes. In our diagram, we can see that the triangles PQD and SLQ are similar, because they have the same shape but different sizes.

We can use the following proportion to find the height of the streetlight:

height of streetlight / distance from person to streetlight = height of person / length of person's shadow

We can plug in the values we know and solve for the height of the streetlight:

h / 480 = 69 / 96
h = (69 / 96) * 480
h = 345

Therefore, the height of the streetlight is 345 inches, or 28.75 feet.

In conclusion, a person who is 69 inches tall stands 40 feet from the base of a streetlight. The streetlight casts a shadow of length 96 inches. Using the concept of similar triangles, we can determine that the streetlight is 345 inches, or 28.75 feet, tall.