A 6-foot person standing 15 feet from a streetlight casts a 10-foot shadow. Two similar triangles are formed. One triangle is formed by the person and the shadow that the person casts. A second triangle is formed by the streetlight and the ground from the base of the streetlight to the end of the shadow.
The street light is __ times taller than the person.
To find out how many times taller the streetlight is compared to the person, we can use the concept of similar triangles.
In this situation, we have two similar triangles formed: one made by the person and their shadow, and the other made by the streetlight and the ground. We can use the properties of similar triangles to find the height relationship between the two.
Let's label the height of the person as h1 and the height of the streetlight as h2. We are trying to find the ratio h2/h1.
According to the information given, we know that the person's height h1 is 6 feet, and the person casts a shadow that is 10 feet long. The distance from the person to the streetlight is 15 feet.
In the first triangle (person and shadow), we have the following relationship:
h1 / 6 ft = shadow length / 10 ft
In the second triangle (streetlight and ground), we have the following relationship:
h2 / ? = distance from streetlight to shadow / 15 ft
We want to find h2 / h1, which will be the ratio of the height of the streetlight to the height of the person.
To solve this, we need to know the distance from the streetlight to the end of the person's shadow. If that distance is known, we can substitute it into the second triangle equation and solve for h2 / h1.
Please provide the distance from the streetlight to the end of the person's shadow so we can proceed with the calculation.