A person who is 6 feet tall walks away from a 50-foot silo toward the tip of the silo's shadow. At a distance of 32 feet from the silo, the person's shadow begins to emerge beyond the silo's shadow.How much farther must the person walk to be completely out of the silo's shadow?
You need to set up the situation with a diagram using similar triangles. Then, use the Pythagorean Theorem.
Let x be the additional distance to the end of the shadow. Using the similar triangles method suggested by Michael, the ratios of the two per[pendicular sides are:
50/(32+x)= 6/x
Solve for x.
50 x = 192 + 6x
44 x = 192
x = ?
To solve this problem, we can use similar triangles. Let's represent the person's height using the letter h and the distance the person walks away from the silo using the letter d.
We are given the following information:
- The person's height is 6 feet.
- The distance from the silo to where the person's shadow begins to emerge is 32 feet.
- The height of the silo is unknown.
Let's set up a ratio of the person's height to the length of their shadow:
h / (d + 32) = 6 / 50
We can cross-multiply to simplify this equation:
h * 50 = 6 * (d + 32)
Now, let's solve for h first:
50h = 6d + 192
Next, let's solve for d by using the information given that the person's shadow begins to emerge beyond the silo's shadow at a distance of 32 feet:
6d + 192 = 6 * (d + 32)
6d + 192 = 6d + 192
0 = 6d - 6d + 192 - 192
0 = 0 + 192 - 192
0 = 0
We have reached an equation with no variable, which means there are infinitely many solutions. This means that the person is already completely out of the silo's shadow at a distance of 32 feet from the silo.
Therefore, the person does not need to walk any farther to be completely out of the silo's shadow.
To solve this problem, we need to use similar triangles. Let's start by setting up the ratios between the person's height, the length of the person's shadow, and the length of the silo's shadow.
Let's assign some labels:
Person's height: A (6 feet)
Person's shadow length: B (unknown)
Silo's shadow length: C (50 feet)
Distance from the silo: D (32 feet)
The remaining distance to be completely out of the silo's shadow: X (unknown)
Now, let's set up the proportion using the similar triangles:
A/B = C/D
Substitute the known values:
6/B = 50/32
Next, cross-multiply and solve for B:
50B = 6 * 32
50B = 192
B = 3.84 feet
So, the length of the person's shadow is approximately 3.84 feet.
To find the remaining distance (X) for the person to be completely out of the silo's shadow, we need to subtract the length of the person's shadow (B) from the total distance from the silo (D):
X = D - B
X = 32 - 3.84
X ≈ 28.16 feet
Therefore, the person must walk approximately 28.16 feet farther to be completely out of the silo's shadow.