# 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.

1. bobpursley

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

2. Scott

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)

3. Henry

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.

4. bobpursley

I agree.

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