Joe is standing on the rooftop of a building that is 100 feet tall.
He looks up to a bird on top of the building next door
The building is 30 feet away from his building. (horizontal distance)
If Joe's angle of elevation to the bird is 32.2º, how far is the bird from the ground?
bird height above building = 30 ft * tan(32.2º)
add in Joe's rooftop height
To find the distance of the bird from the ground, we can use trigonometry.
First, we need to find the height of Joe's eye level above the ground. This can be calculated using the tangent function:
tan(angle) = opposite / adjacent
In this case, the opposite side is the height of the building Joe is standing on (100 feet), and the adjacent side is the horizontal distance between the buildings (30 feet).
So, tan(32.2º) = 100 / 30
Now, we can solve for the height at Joe's eye level:
Height = tan(32.2º) * 30
Height ≈ 52 feet
Therefore, the bird is 52 feet above the ground.