A person who is 5 feet, 6 inches (5.6 feet) tall casts a shadow (from N to S) that is 12 feet long. The distance along the ground from the person (N) to the flagpole (G) is 18 feet. Find the height of the flagpole (FG) showing all calculations.
5 feet, 6 inches = 5.5 ft not 5.6 ft
I don't have your diagram, so have no clue where your N, S etc are, but I can guess that
5.5/12 = height/30
height = 30(5.5/12) = 13.75 ft
= 13 ft, 9 inches
To find the height of the flagpole (FG), we can use similar triangles and the concept of proportions.
Step 1: Understand the problem:
In this problem, we have a person standing (N) who casts a shadow of 12 feet along the ground. We also know that the distance from the person (N) to the flagpole (G) is 18 feet. We need to find the height of the flagpole (FG).
Step 2: Identify the similar triangles:
In this case, we can consider the following two triangles as similar:
1. The triangle formed by the person (N), the top of the person's head (H), and the endpoint of the shadow (S).
2. The triangle formed by the flagpole (F), the top of the flagpole (G), and the endpoint of the shadow (S)
Both triangles have a shared angle at the top of the person's head (H) and the top of the flagpole (G).
Step 3: Set up the proportion:
Let's denote the height of the person as h and the height of the flagpole as x. Since the person's height is given as 5.6 feet, we have h = 5.6 feet.
Now, we can set up the proportion between the corresponding sides of the triangles:
(person's height)/(shadow length) = (flagpole height)/(distance from person to flagpole)
or
h/12 = x/18
Step 4: Solve the proportion for x:
To find x, we can cross-multiply the proportion:
12x = 18h
Substitute the given height of the person (h = 5.6 feet):
12x = 18 * 5.6
Step 5: Calculate x:
Solving the equation:
12x = 100.8
Divide both sides by 12:
x = 100.8/12
x = 8.4
Therefore, the height of the flagpole (FG) is 8.4 feet.
By using the concept of similar triangles and proportions, we determined that the height of the flagpole is 8.4 feet.