Question 1205338
The fact that we are given the height of the pedestal, suggest that the height of the pedestal is relevant.
In real life, we would ask how high the eye of the observer is relative to the base of the pedestal.
Is the observer standing up? How tall is the observer?
Is the ground horizontal between the observer and the bottom of the pedestal?
 
I'll sketch two right triangles with the eye of the observer, the bottom and top of the pedestal, and the top of the flagpole as vertices.
Let {{{h}}} be the height of the flagpole in meters.
 
Observer lying on the grass on horizontal ground {{{drawing(300,330,-5,25,-2,31,
rectangle(-0.5,0,0.5,20),rectangle(-0.1,20,0.1,29.6),
locate(-3,26,flagpole),locate(-3,10,pedestal),
arrow(15,0,40,0),arrow(0,0,-10,0),locate(17,-0.3,horizontal),
arrow(15,5,15,0.5),locate(15,7.8,eye),
locate(18,7.8,of),locate(15,6.5,observer),
green(triangle(0,0,0,29.6,15,0)),green(rectangle(0,0,1,1)),
green(triangle(0,20,0,29.6,15,0)),
red(arc(15,0,10,10,180,233)),locate(11,2.5,red(A)),
red(arc(15,0,30,30,233,243)),locate(6.5,13,red(10^o))
)}}} 
{{{tan(red(A))=20/15}}} --> {{{red(A)=53.13^o}}}
{{{red(A+10^o)=53.13^o+10^o=63.13^o}}}
{{{tan(red(A+10^o))=tan(63.13^o)=1.97367=(20+h)/15}}} --> {{{h=1.97367*15-20}}}
{{{h=highlight(9.6)}}}
 
Note: If I was the observer I would be standing up, with my eye 1.6 m above ground level.
Then, the vertical height of the top of the pedestal above the eye of the observer would be 18.4 m instead of 20 m.
As a consequence, the triangles would have been a little different, and the calculated height of the flagpole would round to only 6.9 m.