a man is standing 30 feet away from a street light. He is casting a shadow that is 10 feet long and he is 4 feet tall. What is the height of the street light?
Plz help me
To find the height of the street light, we can use similar triangles and proportions.
Step 1: Set up the proportion:
Let x be the height of the street light. We can set up the following proportion:
Shadow length / Man's height = Distance from man to street light / Height of street light
Using the given values:
10 feet / 4 feet = 30 feet / x
Step 2: Solve the proportion:
Cross-multiply and solve for x:
10 feet * x = 4 feet * 30 feet
10x = 120 feet
Step 3: Divide both sides by 10:
x = 120 feet / 10
x = 12 feet
Therefore, the height of the street light is 12 feet.
To solve this problem, we can use similar triangles. The height of the man's shadow is proportional to his height and the distance between him and the street light.
Let's set up the proportion using the given measurements:
(man's height) / (man's shadow length) = (street light's height) / (distance between the man and street light)
Given:
(man's height) = 4 feet
(man's shadow length) = 10 feet
(distance between the man and street light) = 30 feet
Plugging in these values into the proportion:
4 feet / 10 feet = (street light's height) / 30 feet
To solve for the street light's height, we can cross multiply:
4 feet * 30 feet = 10 feet * (street light's height)
120 feet = 10 feet * (street light's height)
Now, we can isolate (street light's height) by dividing both sides of the equation by 10 feet:
120 feet / 10 feet = (street light's height)
12 feet = (street light's height)
Therefore, the height of the street light is 12 feet.
using similar triangles,
h/(30+10) = 4/10
now just solve for h