To determine the height of the building, we can use trigonometry. In this case, we can use the tangent function, which relates the angle of elevation to the height and shadow of the object.
The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this scenario:
tan(angle of elevation) = height of building / shadow length
We are given the angle of elevation (43 degrees) and the length of the shadow (20 feet). Let's substitute these values into the equation:
tan(43 degrees) = height of building / 20 feet
To find the height of the building, we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by 20 feet:
20 feet * tan(43 degrees) = height of building
Now we can calculate the height of the building using a calculator:
Height of building = 20 feet * tan(43 degrees) ≈ 20 feet * 0.9205 ≈ 18.41 feet
Therefore, the height of the building that casts a 20-foot shadow with an angle of elevation of 43 degrees is approximately 18.41 feet.