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.
This is a similar triangle proportional equation.
x/1m = 36.72/3.06
or if you want to use the tangent ratio in the smaller triangle you can use the angle found
tanx =1/3.06
and apply it to the larger triangle.
To find the height of the flagpole, we can use the concept of similar triangles.
First, let's label the variables:
- Height of the flagpole: h (in meters)
- Length of the flagpole's shadow: x (in meters)
- Length of the meter stick's shadow: y (in meters)
According to the given information, the length of the flagpole's shadow is 36.72 m, and the length of the meter stick's shadow is 3.06 m.
Using the concept of similar triangles, we can set up the following proportion:
h / x = 1 / (y)
Now substitute the given values:
h / 36.72 = 1 / 3.06
To solve for h, we need to isolate it on one side of the equation. Multiply both sides of the equation by 36.72:
h = (1 / 3.06) * 36.72
Now calculate the expression on the right side of the equation:
h = 12 * 36.72
h = 440.64
Therefore, the height of the flagpole is 440.64 meters.