Heights and Distances

From an aeroplane flying, vertically above a horizontal road, the angles of depression of two consecutive stones on the same side of the aeroplane are observed to be $30^{\circ}$ and $60^{\circ}$ respectively. The…

-The angle of elevation of the top of a TV tower from three points $A, B$ and $C$ in a straight line through the foot of the tower are $\alpha, 2 \alpha$ and $3 \alpha$ respectively. If $A B=a$, then height of the tower…

From the top of a building of height $h$ metre, the angle of depression of an object on the ground is $\theta$. What is the distance (in metre) of the object from the foot of the building?

From the top of a hill $h$ metres high the angles of depressions of the top and the bottom of a pillar are $\alpha$ and $\beta$ respectively. The height (in metres) of the pillar is

The sum of angles of elevation of the top of a tower from two points distant $a$ and $b$ from the base and in the same straight line with it is $90^{\circ}$. Then, the height of the tower is

The semivertical angle of a cone is $45^{\circ}$. If the height of the cone is $20.025 \mathrm{~cm}$, then the approximate value of its lateral surface area (in sq. $\mathrm{cm}$) is

A person observes the top of a tower from a point $A$ on the ground. The elevation of the tower from this point is $60^{\circ}$. He moves $60 \mathrm{~m}$ in the direction perpendicular to the line joining $A$ and base…

A man \(2 $\mathrm{~m}\)$ tall, walks at the rate of \(1 $\frac{2}{3}$ $\mathrm{~m}$ / $\mathrm{s}\)$ towards a street light which is \(5 $\frac{1}{3}$ $\mathrm{~m}\)$ above the ground. The rate at which the length of…

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:

A man of height \(2 $\mathrm{~m}\)$ walks at a uniform speed of \(7 $\mathrm{~m}$ / $\mathrm{min}\)$ away from a lamp post of height \(9 $\mathrm{~m}\).$ The rate $\((\mathrm{m}$ / $\mathrm{min})\)$ at which the length…

The angle of elevation of an object from a point $P$ on the level ground is $\alpha$. Moving $d$ metres on the ground towards the object, the angle of elevation is found to be $\beta$. Then the height (in metres) of the…

A vertical pole subtends an angle $\tan ^{-1}\left(\frac{1}{2}\right)$ at a point $P$ on the ground. If the angles substended by the upper half and the lower half of the pole at $P$ are respectively $\alpha$ and…