From a point A on the ground, the angle of elevation of the top of a 20 m tall building is 45º. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from A is 60º. Find the length of the flagstaff.
Solution
In $\Delta$OAB tan $45^{\circ} = \dfrac{20}{AO}$
In $\Delta$OAC tan $60^{\circ} = \sqrt{3}$
So, AC $= \sqrt{3}$
$\therefore$ Length of flagstaff $= (\sqrt{3} - 1)$
Now, $1 \rightarrow 20$
$(\sqrt{3} - 1) \rightarrow $20(\sqrt{3} - 1)$