trigonometry(height and distance)
posted by Anamika .
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.

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 
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) 
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. 
I agree.
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