In another attempt to determine the height of the flagpole, a metre stick was placed vertically beside the flagpole. When the flagpole’s shadow was 36.72 m long, the metre stick’s shadow was 3.06 m long. Find the height of the flagpole.
h = (36.72m /3.06m) * 1m =
To find the height of the flagpole, we can use similar triangles and the concept of proportions. Here's how you can solve this problem step by step:
Step 1: Set up the proportion
Let's denote the height of the flagpole as 'h' (in meters) and the length of the flagpole's shadow as 'x' (in meters).
We have two similar triangles: one formed by the flagpole and its shadow, and another formed by the meter stick and its shadow. Using the property of similar triangles, we can write the following proportion:
\( \frac{h}{x} = \frac{\text{length of meter stick}}{\text{length of meter stick's shadow}} \)
Step 2: Substitute the known values
We are given that the length of the flagpole's shadow is 36.72 m and the length of the meter stick's shadow is 3.06 m. Substituting these values into the proportion, we get:
\( \frac{h}{36.72} = \frac{1}{3.06} \)
Step 3: Solve for the height of the flagpole
To isolate 'h', we can cross-multiply the equation:
\( h = \frac{36.72 \times 1}{3.06} \)
Simplifying the right side of the equation:
\( h = 12 \)
Thus, the height of the flagpole is 12 meters.
So, the height of the flagpole is 12 meters.