On a level ground, a 5 ft. person and a flagpole cast shadows of 10 feet and 60 feet respectively. What is the height og the flagpole?
done, see your other post above
To find the height of the flagpole, we can use the concept of similar triangles.
Let's consider two triangles: the triangle formed by the person, their shadow, and the ground, and the triangle formed by the flagpole, its shadow, and the ground.
In the first triangle, we have the height of the person (5 ft) and the length of their shadow (10 ft). In the second triangle, we need to find the height of the flagpole (let's call it h) and the length of its shadow (let's call it s).
Since the triangles are similar, we can set up the following proportion:
(height of person) / (length of person's shadow) = (height of flagpole) / (length of flagpole's shadow)
Or in mathematical terms:
5 / 10 = h / s
To solve for h, we need to find s. We know that the person's height is 5 ft, and their shadow is 10 ft. Therefore, the ratio of the person's height to their shadow is 1:2.
Since the person casts a shadow of 10 ft, we can multiply the length of their shadow by the ratio to find the length of the flagpole's shadow:
10 ft * 2 = 20 ft
Now that we have the values for the length of the flagpole's shadow (20 ft) and the person's shadow (10 ft), we can substitute them back into our proportion:
5 / 10 = h / 20
To find h, we can cross-multiply:
5 * 20 = 10 * h
100 = 10h
Simplifying the equation:
10h = 100
Divide both sides by 10:
h = 10
Therefore, the height of the flagpole is 10 ft.