Question

Two trees 7 m and 4 m high stand upright on a ground. If their bases (roots) are 4 m apart, then find the distance between their tops.

Answer 1

Let BE be the smaller tree and AD be the bigger tree. Now, we have to find AB (i.e. the distance between their tops)

By observing,
ED = BC = 4 m and BE = CD = 4 m
In $\Delta ABC$, BC = 4 m
and AC = AD - CD = (7 - 4) m = 3 m
In right angled $\Delta ABC$,
$A{B}^2=A{C}^2+B{C}^2$ [by Pythagoras theorem]
$=4^2+3^2$
$=16+9$
$=25$
$\Rightarrow AB=\sqrt{25}\Rightarrow AB=5m$
Therefore, the distance between their tops is 5 m.