2. A person who is 1.5 meters tall casts a shadow that is 8 meters long. The distance along the ground from the person (N) to the flagpole (G) is 32 meters. Find the height of the flagpole (FG) showing all calculations.
using similar triangles,
1.5/8 = FG/(32+8)
To find the height of the flagpole (FG), we can use the concept of similar triangles.
We have two triangles here: the person's shadow triangle (formed by the person's height, the length of the shadow, and the distance along the ground) and the flagpole's height triangle (formed by the flagpole's height, the flagpole's shadow, and the distance along the ground).
Let's label the person's height H, the person's shadow S, the distance from the person to the flagpole N, and the flagpole's height F.
From the given information, we know that H = 1.5 meters, S = 8 meters, and N = 32 meters.
We want to find F, the height of the flagpole. To do this, we can set up a proportion using the similar triangles:
(H / S) = (F / N)
Now, let's substitute the known values:
(1.5 / 8) = (F / 32)
To solve for F, we can cross-multiply and then divide:
1.5 * 32 = 8F
48 = 8F
F = 48 / 8
F = 6 meters
Therefore, the height of the flagpole is 6 meters.