Mathematics
Mathematics
Problem
An observer who is 1.6\,m tall is standing on level ground 35\,m away from a building. The angle of elevation of the top of the building from his eyes is . Calculate the height of the building.Intuitive explanation
The key is to set up a right triangle using the observer's eye level as your reference point. Since the observer's eyes are 1.6 m above ground, you're measuring the angle of elevation from that height, not from ground level. Use the tangent ratio to find the vertical distance from eye level to the rooftop, then add back the observer's height to get the building's total height.
Intuitive explanation
The key is to set up a right triangle using the observer's eye level as your reference point. Since the observer's eyes are 1.6 m above ground, you're measuring the angle of elevation from that height, not from ground level. Use the tangent ratio to find the vertical distance from eye level to the rooftop, then add back the observer's height to get the building's total height.