The angle of elevation of the top of the tower observed from each of the three points $A, B, C$ on the ground,forming a triangle,is the same angle $\alpha$. If $R$ is the circum-radius of the $\Delta ABC$,then the height of the tower is

$A$ flag-staff of $5 \, m$ high stands on a building of $25 \, m$ high. An observer is at a height of $30 \, m$. The flag-staff and the building subtend equal angles at the observer. The distance of the observer from the top of the flag-staff is

$A$ balloon is observed simultaneously from three points $A, B$ and $C$ on a straight road directly under it. The angular elevation at $B$ is twice and at $C$ is thrice that of $A$. If the distance between $A$ and $B$ is $200$ metres and the distance between $B$ and $C$ is $100$ metres,then the height of the balloon is:

The angle of elevation of the top of a tower from a point $A$ due south of the tower is $\alpha$ and from a point $B$ due east of the tower is $\beta$. If $AB = d$,then the height of the tower is

$A$ $20 \ m$ 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 $\tan \alpha$.

$A$ balloon is descending at a rate of $4 \, m/min$. Its angle of elevation from a point on the ground is $45^\circ$,which reduces to $30^\circ$ after $10 \, minutes$. At what distance from the observer will the balloon touch the ground?