Heights and Distances

If the angles of elevation of the top of a tower from two points at the distances of $3 \mathrm{m}$ and $12 \mathrm{m}$ from the base of the tower in the same straight line with it are complementary, then the height of the tower (in $\mathrm{m}$) is

The angle of elevation of the top of a $H \mathrm{m}$. high tower from two points $A$ and $B$ on the horizontal plane are $60° \text{and} 30°$ respectively. If the distance of $A$ from the foot of the tower is $a \mathrm{m}$. then the distance of $B$ from the foot of the tower will be _____$\mathrm{m}$.

If a flagstaff of $6$ metres height placed on the top of a tower throws a shadow of $2\sqrt{3} \mathrm{m}$ along the ground, then the angle (in degrees) that the sun makes with the ground is

A tree breaks into two parts due to heavy wind such that the upper part makes an angle of  $30°$with plane. The place where the upper part of the tree touches the ground is at a distance of $10\mathrm{m}$ from the base point of the tree. The height of the tree is

A circus artist is climbing on a $20 meter$ long rope which is tightly stretched and tied to the top of a vertical pole. If the angle made by the rope with the ground level is $30°$, then the height of the pole will be _____.

If the shadow of $10$m high tree is $10\sqrt{3}$m, then the angle of elevation of sun is

Angle of elevation of a tower from a point at a distance of $15$ centimeter from foot of the tower is $60°$. Then height of tower is

The string of a kite of length $100 \mathrm{m}$ makes an angle of $60°$ with the horizontal ground. Imaging that there is no slack in the string, the height of the kite from the ground is

The tip of a partially broken tree touches the ground at a point $10 \mathrm{m}$ from foot of it and makes an angle of elevation of $30°$ from the ground. Then, the height of the tree is

The angle of depression of two ships as observed from the top of a $80 m$ high lighthouse from the sea level at $30°$ and $45°$. If two ships are on the same side of the lighthouse and all the three are along at the straight line, then the distance between the two ships is: 

If ratio of length of a vertical rod and length of its shadow is $\sqrt{3}:1$, then the angle of elevation of sun will be

From the top of a building of height$\text{'}h\text{'}$ meter, the angle of elevation of the top of the tower is $\text{'}\alpha \text{'}$ ’ and angle of depression of the foot of the tower is $\text{'}\beta \text{'}.$ The height of the tower is:

From the top of a $60 \mathrm{m}$ high tower, the angles of depression of the top and bottom of pillar are $30°$ and $60°$  respectively. Then the height of the pillar is

ABCD is a square plot of horizontal ground. A pole PQ stands somewhere such that angle of elevation of the top of pole i.e. P from A, B, C is respectively ${60}^{\circ }, {45}^{\circ }, {30}^{\circ },$ if  q is the angle of elevation of the top of the pole at point D then $\tan q=$

PQ is a flagstaff erected in a horizontal playground. Student 'A' find that the pole is towards his north and angle of elevation of the top of a flagstaff, 'P', is ${60}^{\circ }.$Whereas students 'B' who is to the East of student' A' finds that angle of elevation of the top of flag staff 'P' is ${45}^{\circ }.$ If the length of flagstaff PQ is $12 m$ then finds the distance between the students 'A' and 'B'

An aeroplane is flying horizontally at a height of $3150 m$ above a horizontal plane. At a particular instant, it passes another aeroplane vertically below it. At this instant, the angles of elevation of the planes from a point on the ground are ${30}^{\circ }$ and ${60}^{\circ }$. Hence, the distance between the two planes at that instant is 

When any object slides down a frictionless inclined plane it experience an acceleration equal to component of acceleration due to gravity in the direction of inclined plane. What amount of downward force a stone of $100$kg will experience on a slope of $6°$ angle of inclination.$(\sin \theta =\theta =\tan \theta$ when angle is very small and measured in radians; $\pi$ radians $=180°)$ $(Let g=10m/s^2; and \pi =3.15)$.

A person at a point observes that $PQ$ and $QR$ portions of $PQR$ building subtends equal angle at his eye while lying on the grassy patch of the park away from the building. If $PQ$ is $16 m$ then what is height of high rise building.

In a level ground flag staffs of length $6m$ is hoisted over a pedestal if the flag staff subtends an angle of $15°$ at a point $P$ on the level ground and the angle of elevation of top of the pedestal at same point is $60°$.What is the height of pedestal ?

The shadow of an upright Deodar tree on the slope of a hill having inclination of $30°$  is $5$ m.Find the tangent of angle of elevation of top of the tree if the length of tree is $20m$.