A man walks directly from point A towards the foot of a tall building 240m away. After covering 180m, he observes that the angle of the top of the building is 45. Determine the angle of elevation of the top of the building from A.
since the angle from 240-180=60 feet away is 45 degrees, the height is 60.
SO, if the angle is x, we have
tan(x) = 60/240
Now just find x.
14.04
Bloemfontein
man walks directly from point A towards the foot of a tall building 240m away. After covering 180m, he observes that the angle of the top of the building is 45. Determine the angle of elevation of the top of the building from A.
I don't have an answer
To determine the angle of elevation of the top of the building from point A, we can use trigonometry, specifically the tangent function.
Let's label the angle of elevation of the top of the building from point A as θ.
Since the man observes that the angle of the top of the building is 45 degrees when he is 180m away from point A, we can use this information.
Using the tangent function: tan(θ) = opposite/adjacent
In this case, the opposite side is the height of the building, and the adjacent side is the distance the man has covered (180m). Therefore, we have:
tan(45) = height of the building / 180m
To find the height of the building, we can rearrange the equation:
height of the building = 180m * tan(45)
Calculating the height of the building: height = 180m * tan(45) = 180m * 1 = 180m
Now that we know the height of the building is 180 meters, we can determine the angle of elevation from point A. Since the opposite side (height) is the same length as the adjacent side (240m), the angle of elevation can be found using the arctangent function:
θ = arctan(180m/240m)
Calculating the angle of elevation: θ = arctan(0.75) ≈ 36.87 degrees
Therefore, the angle of elevation of the top of the building from point A is approximately 36.87 degrees.