The angle of elevation of a tower at a point distant $d$ meters from its base is $30^\circ$. If the tower is $20$ meters high,then the value of $d$ is

If a flag-staff of $6 \ m$ high placed on the top of a tower throws a shadow of $2 \sqrt{3} \ m$ along the ground,then the angle (in degrees) that the sun makes with the ground is.....$^o$

The tops of two poles of height $20 \ m$ and $14 \ m$ are connected by a wire. If the wire makes an angle $30^{\circ}$ with the horizontal,then the length of the wire is $... \ m$.

$A$ $20 \ m$ high flag pole is fixed on an $80 \ m$ high pillar. At a point on the ground $50 \ m$ away from the base of the pillar,the flag pole subtends an angle $\alpha$. Find the value of $\tan \alpha$.

$A$ vertical pole (more than $100 \, ft$ high) consists of two portions,the lower being one-third of the whole. If the upper portion subtends an angle $\tan^{-1}(\frac{1}{2})$ at a point in a horizontal plane through the foot of the pole and at a distance of $40 \, ft$ from it,then the height of the pole is......$ft$.

The angle of elevation of the top of a vertical tower from a point $A$,due east of it,is $45^\circ$. The angle of elevation of the top of the same tower from a point $B$,due south of $A$,is $30^\circ$. If the distance between $A$ and $B$ is $54\sqrt{2} \, \text{m}$,then the height of the tower (in metres) is: