1. Trig Word Problem

Hi, i am having trouble with this problem. A man is standing 35 m from a government building. on top of the building is a Canadian flag. From the man, the angle of elevation of the top of building is pie/6 radians and the angle of elevation of the top of the flag is pie/3 radians. Determine an exact expression for the distance from the top of the flag to the top of the building

2. Fill in the blanks:

$\tan\left[\frac{\pi}{6}\right] =$ ________________

$\tan\left[\frac{\pi}{3}\right] =$ ________________

Thgougth Question: Does the height of the observer make any difference?

3. Suppose x is a hight of the pole of the flag and y be the hight of building,

then the first equation..

$\tan\frac{\pi}{6}=\frac{y}{35}$

$\therefore\frac{1}{\sqrt 3}=\frac{y}{35}$

$\therefore y\sqrt 3=35$

$\therefore y=\frac{35}{\sqrt3}$

and the second will

$\tan\frac{\pi}{3}=\frac{x+y}{35}$

$\therefore\sqrt 3=\frac{x+y}{35}$

$\therefore x+y = 35\sqrt 3$

$\therefore x+\frac{35}{\sqrt3} = 35\sqrt 3$

$\therefore x = 35\sqrt 3 - \frac{35}{\sqrt3}$

find this value, which is the hight of pole..