the shadow of a tower standing on a level ground is found to be 20 m longer when the sun 's altitude is 30 degree than when it is 45 degree.Find the height of the tower.

Tan 45⁰=AB/BC

Since, Tan 45⁰=1

So, AB=BC= h Metres

In Triangle ABD

Tan 30⁰= AB/BD

1/(root)3= h/ h+20

h+20 = h (root)3

20= h(root)3 - h

20 = h[(root)3 - 1]

This Implies, h = 20/[(root)3 - 1]

h = 20*[(root)3+1]/ (3 -1)

On Solving This,

h = 10 [(root)3 + 1]

Hope My answer is correct and You would get to understand this problem more easily with the help of this Diagram...