A person who is 6 feet tall walks away from a 50-foot tower toward the tip of the tower's shadow. At a distance of 32 feet from the tower, the person's shadow begins to emerge beyond the tower's shadow. How much farter must the person walk to be completely out of the tower's shadow?
11=x
To determine how much farther the person must walk to be completely out of the tower's shadow, we can use similar triangles. Let's call the distance the person has already walked away from the tower as "x".
We have two similar right triangles - one formed by the person, their shadow, and the distance they have walked, and the other formed by the tower, its shadow, and the distance from the tower.
The height of the person is 6 feet, and the distance from the tower is 32 feet. The height of the tower is 50 feet.
Since the triangles are similar, we can set up a proportion:
(height of person) / (distance from tower) = (height of tower) / (length of tower's shadow)
Using the given values, we get:
6 / x = 50 / 32
Now, we can cross-multiply to solve for x:
6 * 32 = 50 * x
192 = 50x
Dividing both sides by 50:
x = 192 / 50
x = 3.84
Therefore, the person must walk an additional 3.84 feet to be completely out of the tower's shadow.
To find out how much farther the person must walk to be completely out of the tower's shadow, we need to understand the concept of similar triangles.
First, let's analyze the situation. We have a person who is 6 feet tall walking away from a 50-foot tower. As the person moves away from the tower, their shadow starts to extend beyond the tower's shadow.
We can consider two similar triangles. The first triangle is formed by the person, the person's shadow, and the distance they have walked. Let's call the height of the person's shadow "x".
The second triangle is formed by the tower, the tower's shadow, and the distance between the person and the tower. In this triangle, the height of the tower is 50 feet, the length of its shadow is unknown, and the distance between the person and the tower is 32 feet.
Since the triangles are similar, their corresponding sides have the same ratio. We can set up the following proportion:
(person's height) / (person's shadow) = (tower's height) / (tower's shadow)
Or in equation form:
6 / x = 50 / (x + 32)
We can cross-multiply to solve for x:
6(x + 32) = 50x
Simplifying the equation:
6x + 192 = 50x
Rearranging:
50x - 6x = 192
44x = 192
Dividing both sides by 44:
x = 192 / 44
x ≈ 4.364
Therefore, the person's shadow height is approximately 4.364 feet.
To find out how much farther the person must walk to be completely out of the tower's shadow, we need to determine the remaining length of the tower's shadow. This can be done by subtracting the length of the person's shadow from the distance between the person and the tower.
Remaining length of the tower's shadow = (Distance between person and tower) - (Person's shadow)
Remaining length of the tower's shadow = 32 - 4.364 ≈ 27.636 feet
So, the person must walk an additional approximately 27.636 feet to be completely out of the tower's shadow.