A 6 m flagpole casts a 5 m shadow at the same
time of the day as a building casts a 28m
shadow. How tall is the building?
I drew out a flag and a building, with a shadow coming from the top to the ground. What do i do next?
Use proportions.
The height of the building can be x.
6/5=x/28
Cross multiply.
6*28=5x
168=5x
Divide each side by 5 so you isolate x.
168/5=x
168/5 = Simplify this to get your answer.
33.6
Great start! Now, let's use the concept of similar triangles to solve this problem.
First, we need to understand that the two triangles formed by the flagpole and its shadow, and the building and its shadow, are similar triangles. This means that their corresponding sides are proportional, allowing us to set up a proportion.
In this case, we can set up the following proportion:
(flagpole height) / (flagpole shadow) = (building height) / (building shadow)
Now, we can substitute the values:
6 m / 5 m = (building height) / 28 m
To find the height of the building, we need to solve for (building height). To do this, we can use cross multiplication.
Cross multiplying the proportion, we get:
(6 m) * (28 m) = (5 m) * (building height)
168 m² = 5 m * (building height)
Next, divide both sides of the equation by 5 m to isolate the (building height):
168 m² / 5 m = building height
Now, perform the calculation:
33.6 m = building height
Therefore, the building is approximately 33.6 meters tall.