a person 5 feet tall casts a shadow 8 feet long. At the same time of day. a lamppost casts a shadow 18 feet long. Using similar triangles and proportions, find the height of the lamp
5 / 8 = h / 18, solve for h
To find the height of the lamp, we can set up a proportion using similar triangles.
Let's denote the height of the lamp as "h".
According to the given information, we have:
Height of the person (p) = 5 feet
Length of the person's shadow (s1) = 8 feet
Length of the lamp's shadow (s2) = 18 feet
Now, we can set up the proportion between the person and the lamp:
(p / s1) = (h / s2)
Substituting the given values, we get:
(5 / 8) = (h / 18)
To find "h", we can cross multiply and solve for it:
5 * 18 = 8 * h
90 = 8h
Now, divide both sides by 8:
90 / 8 = h
The height of the lamp is approximately 11.25 feet.
To find the height of the lamppost, we will use the concept of similar triangles and proportions.
Let's assign variables to the given measurements:
The height of the person: x feet
The length of the person's shadow: y feet
The length of the lamppost's shadow: z feet
We can set up a proportion using the similar triangles formed by the person, their shadow, and the lamppost:
Height of the person / Length of the person's shadow = Height of the lamppost / Length of the lamppost's shadow
Using the given information:
x / y = Height of the lamppost / z
Substituting the values from the problem:
5 / 8 = Height of the lamppost / 18
To solve this proportion, we can cross-multiply:
5 * 18 = 8 * (Height of the lamppost)
90 = 8 * (Height of the lamppost)
Now, to find the height of the lamppost, divide both sides of the equation by 8:
Height of the lamppost = 90 / 8
Height of the lamppost = 11.25 feet
Therefore, the height of the lamppost is 11.25 feet.