Question

A flagstaff stands on the top of a $5$ m high tower. From a point on the ground, the angle of elevation of the top of the flagstaff is ${60}^0$ and from the same point, the angle of elevation of the top of the tower is ${45}^0$. Find the height of the flagstaff.

Answer 1

Given the Height of the Tower $BC=5m$

Let the height of the Flagstaff be $=AB$

Now, in $△BCD$

$\tan {45}^o=\frac{BC}{CD}=\frac{5}{CD}\Rightarrow CD=5$

and in $△ACD$

$\tan {60}^o=\frac{AB+BC}{CD}=\frac{AB+5}{5}\Rightarrow AB+5=5\sqrt{3}\Rightarrow AB=5\sqrt{3}-5=3.65m$