Question

The shadow of a tower when the angle of elevation of the sun is 45o is found to be 10 m longer than when it is 60º. Find the height of the tower

Answer 1

Then?

Answer 2

wait. I drew the picture wrong.

Answer 3

In the triangle on the RHS, tan(60) = h/x = sqrt(3)

Answer 4

Now in the big triangle, tan(45) = h/ (x+10)

Answer 5

This gives two eqns

\[x+10 = h\]

\[x= \frac{h}{\sqrt{3}}\]

Answer 6

h= h/ sqrt{3} +10

h [ 1- 1/ sqrt{3}] =10

Answer 7

\[h= \frac{10}{ 1- \frac{1}{\sqrt{3}}}\]

Answer 8

h=23.66m