A flagpole that is 21 feet tall casts a shadow of 9 1/3 feet. If the steeple of a nearby church cast a shadow of 57 feet at the same time, how tall is the church?
x / 57 = 21 / (9 1/3)
21/(9 1/3) / x/57
Cross multiply and solve for x.
To find the height of the church, we can use a proportion since we have a similar triangle situation.
Let's set up a proportion between the flagpole and the church steeple shadows:
Height of Flagpole / Length of Flagpole Shadow = Height of Church / Length of Church Shadow
We know that the height of the flagpole is 21 feet and the length of its shadow is 9 1/3 feet. We also know that the length of the church shadow is 57 feet.
Plugging in these values, we get:
21 feet / 9 1/3 feet = Height of Church / 57 feet
To make calculations easier, let's convert the mixed number 9 1/3 to an improper fraction.
9 1/3 feet is equal to (3 * 9 + 1) / 3 = 28/3 feet.
So, our proportion becomes:
21 feet / (28/3) feet = Height of Church / 57 feet
To solve for the height of the church, we can cross multiply and then solve for the unknown value:
(21 feet * 57 feet) / (28/3) feet = Height of Church
To multiply fractions, we multiply the numerators and denominators straight across:
(21 * 57) / (28/3) feet = Height of Church
By multiplying the whole numbers and dividing by the fraction, we get:
1197 / (28/3) feet = Height of Church
To divide a fraction, we multiply by its reciprocal:
1197 * (3/28) feet = Height of Church
Now, let's simplify this multiplication:
1197 * 3 / 28 feet = Height of Church
3558 / 28 feet = Height of Church
Now, let's simplify this fraction:
127.07142857 feet = Height of Church (rounded to the nearest hundredth)
So, the height of the church is approximately 127.07 feet.