Question

Sven has an old windmill on his farm located 200ft from his house. The windmill has started to lean and is presently leaning 5 degrees from vertical towards the house. Sven measured the angle of elevation from the house to the top of the windmill up to be 55 degrees. Based upon this information, determine the height of the windmill and whether or not Sven should be wooried about the windmill landing on his house should it topple over.

Answer 1

The height of the windmill is approximately 17.42 feet. Sven does not need to worry about the windmill landing on his house.

Step-by-step explanation:

To determine the height of the windmill, we can use trigonometry. Given that the windmill is leaning 5 degrees from vertical towards the house, we can consider this as the angle of depression from the top of the windmill to the base of the windmill. We can use the tangent function to find the height of the windmill. Let's call the height h.

tan(5) = h / 200ft

h = 200ft * tan(5)

h ≈ 17.42ft

Therefore, the height of the windmill is approximately 17.42 feet.

To determine whether Sven should be worried about the windmill landing on his house, we need to consider the distance between the windmill and the house. Since the windmill is leaning towards the house, the height of the windmill will decrease as it leans further. However, based on the given information, the windmill's height is less than the distance between the windmill and the house, so it is unlikely that the windmill will land on the house.