We have two similar triangles, the one as a whole and the one inside of it. To calculate the height of the flagpole we can set up a proportion. First calculate the length of the base of the smaller triangle.
16.60 - 12.45 = 4.15m
The height is 1.65m, set up a proportion:
[tex]\sf\dfrac{1.65}{4.15}=\dfrac{x}{16.60}[/tex]
Cross multiply:
[tex]\sf 27.39=4.15x[/tex]
Divide 4.15 to both sides:
[tex]\sf x=\boxed{\sf 6.6m}[/tex]
So the height of the flagpole is 6.6 meters tall.
