A 4.5 ft mailbox post casts a 6 ft shadow. A nearby flagpole casts an 20 ft shadow. How tall is the flagpole?
4.5 / 6 = x / 20
Cross multiply and solve for x.
To find the height of the flagpole, we can use the concept of similar triangles. Similar triangles have proportional sides, which means we can set up a ratio between the lengths of the mailbox post and its shadow, and the lengths of the flagpole and its shadow.
Let's assign variables to the heights of the mailbox post (M) and the flagpole (F), and the lengths of their respective shadows, (S1 for the post and S2 for the flagpole).
Given:
Height of mailbox post (M) = 4.5 ft
Length of shadow of mailbox post (S1) = 6 ft
Length of shadow of flagpole (S2) = 20 ft
We can set up the following ratio:
M/S1 = F/S2
Now, let's plug in the values:
4.5/6 = F/20
Now, we can solve for F:
First, cross-multiply:
4.5 * 20 = 6 * F
90 = 6F
Next, divide both sides by 6 to isolate F:
90/6 = F
15 = F
Therefore, the height of the flagpole (F) is 15 ft.