Class 10 · Chapter 9 · Interactive Lab
A tower, a kite string, a bridge over a river — every one becomes a right triangle the moment you draw a line of sight. Adjust the sliders below and watch the same trigonometric ratios from the last chapter go to work measuring things nobody actually climbed to measure.
The line of sight runs from the observer's eye to the object. When the object is above the horizontal, that angle is the angle of elevation — raise your head. When it's below, it's the angle of depression — lower your head. Move the object to see both.
drag the sliders to move the object
Just like the tower and chimney examples: stand a known distance away, measure the angle of elevation to the top, and tan(angle) = height ⁄ distance gives you the rest. Add an observer eye-height to match problems like the chimney example, where the sighting doesn't start at ground level.
tower height solved from distance + angle of elevation
Stand at one point P and sight two angles from there: one to the top of the building (known height), one to the top of whatever sits on it. The first angle fixes your distance from the building; the second, applied to that same distance, gives the full height.
building height is fixed · both angles sighted from the same point P
From a bridge, lighthouse, or tall building, sight two angles of depression. If both points are on the same side, subtracting the two horizontal distances gives the distance between them (like two ships). If they're on opposite sides, adding the distances gives the width between them (like a river).
height is fixed · switch mode to change what's being measured