a fence 2m tall and 5m from a parallel building - what length is the shadow from the fence and how is this worked out?
To find the length of the shadow from the fence, we can use similar triangles. Here's how to work it out step by step:
Step 1: Understand the problem
We have a fence that is 2m tall and located 5m from a parallel building. We want to find the length of the shadow cast by the fence.
Step 2: Identify the similar triangles
Since the fence and its shadow are parallel to the building, we can create two similar triangles. One triangle is formed by the fence, its shadow, and the building, while the other triangle is formed by the building, its height, and the fence's shadow.
Step 3: Set up the ratios
We can set up a ratio to compare the corresponding sides of the two similar triangles. Let's choose to compare the height of the fence to the length of its shadow.
Let h be the height of the fence, s be the length of its shadow, and b be the height of the building.
In the smaller triangle (formed by the fence, its shadow, and the building):
h/b = s/(b + s)
Step 4: Substitute known values
We are given that the fence is 2m tall (h = 2m) and the fence is located 5m from the building (b = 5m).
2/5 = s/(5 + s)
Step 5: Solve for s
To solve for s, we can cross-multiply and solve the resulting equation:
2(5 + s) = 5s
10 + 2s = 5s
10 = 5s - 2s
3s = 10
s = 10/3
Therefore, the length of the shadow cast by the fence is approximately 3.33 meters.
Note: The answer is rounded to two decimal places for convenience.