If a person is 66 inches tall is standing 15 feet away from a streetlight. If the person casts a shadow 84 inches long, how tall is the streetlight?
Let X be the streetlight height.
84 inches is 7.00 feet.
66 inches is 5.50 feet.
Draw a figure with a light ray passing from the light, skimming the top of the person's head and striking the ground at the end of the shadow.
Because of similar triangles,
H/(15 + 7) = 5.5/7
H = 22*(11/14) = 17.29 feet
Sorry, the question is "A person is 66 inches tall is standing 15 feet away from a streetlight. If the person casts a shadow 84 inches long, how tall is the streetlight?"
Well, let's shed some light on this problem! If the person is 66 inches tall and their shadow is 84 inches long, we can use a little math magic to figure out the height of the streetlight.
We can set up a proportion:
Person's height / Person's shadow length = Streetlight's height / Streetlight's shadow length
So, in this case, it would be:
66 / 84 = Streetlight's height / 15
Now we just cross-multiply and solve for Streetlight's height:
84 * Streetlight's height = 66 * 15
And after performing some mathematical gymnastics, we find that the height of the streetlight should be approximately 11.43 feet. That's one pretty tall streetlight!
To find the height of the streetlight, we can use similar triangles. The person, the person's shadow, and the streetlight form a right triangle.
Let's represent the height of the person as "x" and the height of the streetlight as "h".
Using the similar triangle property, we can set up the following ratio:
(person's height) / (person's shadow length) = (streetlight's height) / (distance between person and streetlight)
Plugging in the given values:
x / 84 inches = h / 15 feet
Since the height of the person is given as 66 inches, we can substitute x with 66:
66 / 84 inches = h / 15 feet
Now let's convert inches to feet:
66 / 84 * 1 foot = h / 15 feet
0.7857 feet = h / 15 feet
To isolate "h" on one side of the equation, we can multiply both sides by 15:
0.7857 feet * 15 = h
11.8 feet = h
Therefore, the streetlight is approximately 11.8 feet tall.
To calculate the height of the streetlight, we can use similar triangles. Let's set up a proportion:
Height of the person / Length of the person's shadow = Height of the streetlight / Length of the streetlight's shadow
First, let's convert the person's height and the length of their shadow to the same unit of measurement. Both are currently given in inches, so let's keep it consistent.
The person is 66 inches tall, and their shadow is 84 inches long. Now, let's convert the person's height and shadow length to feet to make the calculations easier. Since there are 12 inches in a foot, we divide both measurements by 12.
Person's height: 66 inches / 12 inches per foot = 5.5 feet
Shadow length: 84 inches / 12 inches per foot = 7 feet
Now, the proportion can be set up:
5.5 feet / 7 feet = Height of the streetlight / 15 feet
To solve for the height of the streetlight, cross-multiply and divide:
(5.5 feet * 15 feet) / 7 feet = Height of the streetlight
Calculating this expression: (5.5 * 15) / 7 = 11.7857 feet
So, the height of the streetlight is approximately 11.79 feet.