roger is 5 feet tall and casts a shadow 3.5 feet longer. at the same time,the flagpole outside his school casts a shadow 14 feet long. write and solve a proportion to find the height of the flagpole.
well I always start by drawing a small diagram just to help you visualize. you can see that you need to set a proportion of
Rogers height Poles height
_____________ = ______________
Rogers shadow Poles shadow
5 P
_ = __
3.5 15
now you can cross multiply
5(15)=3.5(P)
75=3.5P
P= 21.4 feet tall
since the height/shadow ratio is the same
5/3.5 = h/14
or, just note that the pole's shadow id 4 times as long, so the pole is 4 times as tall.
Let's set up a proportion to find the height of the flagpole.
We can set up the proportion using the relationship between the height of Roger and the length of his shadow, and the height of the flagpole and the length of its shadow. The proportion can be written as:
(Roger's height) / (Length of Roger's shadow) = (Height of flagpole) / (Length of flagpole's shadow)
Substituting the given values:
(5 feet) / (5 feet + 3.5 feet) = (Height of flagpole) / (14 feet)
Simplifying this proportion:
5 feet / 8.5 feet = (Height of flagpole) / 14 feet
Now, cross-multiply:
(5 feet) * (14 feet) = (8.5 feet) * (Height of flagpole)
70 = 8.5 * (Height of flagpole)
To find the height of the flagpole, divide both sides of the equation by 8.5:
70 / 8.5 = Height of flagpole
Height of flagpole ≈ 8.24 feet
Therefore, the height of the flagpole is approximately 8.24 feet.
To find the height of the flagpole, we can set up a proportion based on the relationship between the heights and the corresponding shadow lengths.
Let's define:
- h as the height of the flagpole
- s as the length of Roger's shadow
Based on the given information, we know that Roger's height is 5 feet and his shadow is 3.5 feet longer than his height. So Roger's shadow length can be calculated as:
s = 5 + 3.5
s = 8.5 feet
We are also given that the flagpole's shadow length is 14 feet.
Now, we can set up the proportion:
(height of Roger) / (length of Roger's shadow) = (height of flagpole) / (length of flagpole's shadow)
Plugging in the values we have:
5 / 8.5 = h / 14
To solve for h, we can cross-multiply and then solve for it:
5 * 14 = 8.5 * h
70 = 8.5h
Finally, divide both sides of the equation by 8.5 to isolate h:
h = 70 / 8.5
Using a calculator, we find that h is approximately 8.24 feet.
Therefore, the height of the flagpole is approximately 8.24 feet.