THIS IS NOTHING TO DO WITH A LADDER
A fence 3m tall is erected vertically and parallel to a building that is 10m away
please can someone tell me the maximum length of the shadow the fence will cast on the ground - thank you
If the sun is behind the building, and the building's height is h, then the longest shadow (s) cast by the fence is when the sun is just about to go down behind the building.
s/3 = (s+10)/h
If the sun is not directly behind the building, then all bets are off.
To find the maximum length of the shadow cast by the fence, we can use similar triangles and basic geometry.
In this situation, we have a right triangle formed by the fence, the ground, and the shadow. The height of the fence acts as the height of the triangle, and the distance between the fence and the building acts as the base of the triangle.
Given that the fence is 3m tall and the building is 10m away, we can set up a proportion to find the length of the shadow (x) cast by the fence:
3m (height of the fence) / x (length of the shadow) = 10m (distance of the building) / (x + 10m) (total distance traveled by the shadow on the ground)
To solve for x, we can cross-multiply and solve the resulting equation:
3m * (x + 10m) = 10m * x
3x + 30m = 10x
30m = 7x
x = 30m / 7 ≈ 4.29m
Therefore, the maximum length of the shadow cast by the fence on the ground is approximately 4.29m.