Angle of Depression

If at some time of the day the ratio of the height of a vertically standing pole to the length of its shadow on the ground is $\sqrt{3}:1$ then find the angle of elevation of the sun at that time.

From the top of a hill, the angles of depression of two consecutive kilometre stones due east are found to be $45°$ and $30°$ respectively. Find the height of the hill in $\mathrm{km}$.

An observer $1.5 \mathrm{m}$ tall is $28.5 \mathrm{m}$ away from a tower and the angle of elevation of the top of the tower from the eye of the observer is $45°$. The height of the tower is

If the elevation of the sun changes from $30°$ to $60°$then the difference between the lengths of shadow as of a pole $15 \mathrm{m}$ high, is

From the top of a hill, the angles of depression of two consecutive $\mathrm{km}$ stones due east are found to be $30°$ and $45°$. The height of the hill is

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

The angle of elevation of the top of a tower from a point on the ground $30 \mathrm{m}$ away from the foot of the tower is $30°$. The height of the tower is 

In a rectangle, the angle between a diagonal and a side is $30°$ and the length of this diagonal is $8 \mathrm{cm}$. The area of the rectangle is,

The tops of two towers of heights $x$ and $y$, standing on a level ground subtend angles of $30°$ and $60°$ respectively at the centre of the line joining their feet. Then, $x:y$ is

On the level ground, the angle of elevation of a tower is $30°$. On moving $20 \mathrm{m}$ nearer, the angle of elevation is $60°$. The height of the tower is

In the given figure, a tower $AB$ is $20 \mathrm{m}$ high and its shadow $BC$ on the ground is $20\sqrt{3} \mathrm{m}$ long. The sun's altitude is 

A pole casts a shadow of length $2\sqrt{3} \mathrm{m}$ on the ground when the sun's elevation is ${60}^{°}$. The height of the pole is 

If the angles of elevation of the top of a tower at two points of distances $a$ and $b$ from the base and in the same straight line with it are complementary, then the height of the tower is

The lengths of a vertical rod and its shadow are in the ratio $1:\sqrt{3}$. The angle of elevation of the sun is 

The length of the shadow of a tower standing on level ground is found to be $2x$ metres longer when the sun's elevation is $30°$ than when it was $45°$. The height of the tower is 

If a $1.5 \mathrm{m}$ tall girl stands at a distance of $3 \mathrm{m}$ from a lamp-post and casts a shadow of length $4.5 \mathrm{m}$ on the ground, then the height of the lamp-post is 

From the top of a cliff $20 \mathrm{m}$ high, the angle of elevation of the top of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is 

A kite is flying at a height of $30 \mathrm{m}$ from the ground. The length of string from the kite to the ground is $60 \mathrm{m}$. Assuming that there is no slack in the string, the angle of elevation of the kite at the ground is 

The angle of depression of car parked on the road from the top of a $150 \mathrm{m}$ high tower is $30°$. The distance of the car from the tower is 

From a point on the ground, $30 \mathrm{m}$ away from the foot of a tower the angle of elevation of the top of the tower is $30°$. The height of the tower is