The shadow of a tower when the angle of elevation of the sun is 45 degree is found to be 5m longer when it is 60 degree. Find the height of the tower.

Answer 1

sin45=h/(d)
sin60=h/(d+5)

h/d=.707
h/(d+5)=.866

d=h*1.414
so
h=(h*1.414+5)*.866
solve for h

Answer 2

the wording of the problem is awkward, but a steeper angle means a shorter shadow

h/(s + 5) = tan(45º) ... h = s + 5
... s = h - 5

h / s = tan(60º)

h = h tan(60º) - 5 tan(60º)

5 tan(60º) = h [tan(60º) - 1)

Answer 3

The distance should be 5m LONGER at 45o.
Tan 45 = h/(d+5).
h = (d+5)*Tan45 = d+5.

Tan60 = h/d.
h = d*Tan60 = 1.73d

d+5 = 1.73d.
d = 6.83 m.

h = d + 5 = 6.83+5 = 11.83 m.

Answer 4

I agree.