In the figure,$\theta_1+\theta_2=\frac{\pi}{2}$ and $\sqrt{3}(BE)=4(AB)$. If the area of $\triangle CAB$ is $2\sqrt{3}-3 \text{ unit}^2$,when $\frac{\theta_2}{\theta_1}$ is the largest,then the perimeter (in unit) of $\triangle CED$ is equal to $...........$.

From the bottom of a pole of height $h,$ the angle of elevation of the top of a tower is $\alpha$ and the pole subtends an angle $\beta$ at the top of the tower. The height of the tower is

The angle of elevation of the top of a mobile tower from three points $P, Q$ and $R$ (on a straight line through the foot of the tower) are $\alpha, \beta$ and $\gamma$ respectively. If all three points lie on the same side of the foot of the tower and $\alpha : \beta : \gamma = 1 : 2 : 3$ and $PQ = l$,then the height of the tower is -

$A$ tower subtends angles $\alpha, 2 \alpha$ and $3 \alpha$ respectively at points $A, B$ and $C$, all lying on a horizontal line through the foot of the tower. Then $\frac{A B}{B C}$ is equal to:

Let $10$ vertical poles standing at equal distances on a straight line,subtend the same angle of elevation $\alpha$ at a point $O$ on this line and all the poles are on the same side of $O$. If the height of the longest pole is $h$ and the distance of the foot of the smallest pole from $O$ is $a$,then the distance between two consecutive poles is:

The top of a hill observed from the top and bottom of a building of height $h$ is at the angle of elevation $p$ and $q$ respectively. The height of the hill is