riposting this.

the answer kindly supplied by Steve is beyond my understanding.

all i want to know please is how long will the shadow be cast on the ground by a 3m tall vertical fence with the sun behind it as follows:

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

Steve's answer makes perfect sense to me, I would do it the same way not knowing the height of the building.

If you forgot to state the height of the building, just plug in the value for h, and solve for s
in Steve's equation:
s/3 = (s+10)/h

e.g. if h = 25m
s/3 = (s+10)/25
25s = 3s + 30
22s = 30
s = 30/22 = appr 1.36 m

To calculate the maximum length of the shadow cast by the 3m tall fence, you will need to consider the angle of elevation of the sun and the distance between the fence and the building.

To determine the angle of elevation of the sun, you can refer to online resources such as sun position calculators or tables for your specific location and date. Alternatively, you can use a clinometer or a smartphone app with a built-in inclinometer to measure the angle directly.

Once you have the angle of elevation, you can use basic trigonometry to calculate the length of the shadow. Here's how:

1. First, visualize the situation: Draw a right-angled triangle with the vertical fence as the height (3m) and the length of the shadow as the base. The angle of elevation from the top of the fence to the sun will be the angle opposite to the height.

2. Determine the length of the adjacent side: Calculate the distance between the fence and the building (10m in this case), and this will be the length of the adjacent side of the triangle.

3. Use the tangent function: Since you have the lengths of the opposite and adjacent sides of the triangle, you can use the tangent function (tan) to find the angle of elevation. The formula is: tan(angle) = opposite / adjacent

4. Solve for the opposite side: Rearrange the formula to solve for the opposite side (length of the shadow). Multiply the adjacent side (10m) by the tangent of the angle to find the length of the shadow.

By following these steps, you should be able to determine the maximum length of the shadow cast by the 3m tall fence.