Let the height of the tree = h

Let the width of the river =w

Angle of elevation when standing on the bank = 60∘

When moved 40 m away from the bank, angle of elevation = 60∘

Now, tan∠ of elevation=\(height\over distance\)

now tan60 =\(h\over w\)

tan60=\(\sqrt3\)

h=w\(\sqrt3\) -(1)

Also tan30=\(h\over w+40\)

h=\(w+40\over\sqrt 3\) -(2)

from equation 1 and 2

\({w\sqrt3}={ w+40\over \sqrt3}\)

\(3w=w+40\)

w=20 m

And , height =\(w\sqrt3=20\sqrt3m=34.6m\)

Height of the tree=34.64 m and width of the river=20m