The length of the shadow of a tree 8m high, when the sun's elevation is 45⁰ , is .......

A 6m tall tree casts a shadow of length 4m.If at the same time  a flagpole casts a shadow 50m in length, then the length of the flagpole is...........

The length of the shadow of a tree 10 high, when the sun's elevation is 30⁰ , is ..........

A 6m long pole casts a shadow of 4m long.At the same time a tree casts a shadow of 28m long, then length of tree is.......

If the horizontal distance between the two trees 20m and 28m high is 15m, then distance between their tops is........

The angle of elevation of the top of a tower is 60⁰.If the height of the tower is doubled, then the angle of elevation of its top will also doubled.

If a man standing on a platform 5m above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.

The length of the shadow of a tree 12m high, when sun's elevation is 45⁰, is \(12\sqrt{3}\)m

Theodolite is an instrument used for measuring the angles of elevation and depression with a rotating telescope.

The angle of elevation of the top of a tower from a point 20 meters away from the base is 45^o . Find the height of the tower.

A tower stands vertically on the ground. From a point on the ground 100 m away from the foot of the tower, the angle of elevation of the top of the tower is 45^o . Find the height of the tower.

Find the length of the shadow of a 20 m tall pole, on the ground when the sun's elevation is 45^o .

A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60\(\unicode{xb0} \) and from the same point the angle of elevation of the top of the pedestal is 45\(\unicode{xb0} \). Find the height of the pedestal.

As observed from the top of a 75 m high lighthouse from the sea - level, the angles of depression of two ships are 30\(\unicode{xb0} \) and 45\(\unicode{xb0} \). If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.

If a pole 6 m high throws shadow of \(2\sqrt { 3 } \) m, then find the angle of elevation of the sun.

A man on the deck of a ship, 12 m above water level, observes that the angle of elevation of the top of a cliff is 60^o and the angle of depression of the base of the cliff is 30^o. Find the distance of the cliff from the ship and the height of the cliff. \((Use\sqrt { 3 } =1.732)\)

At a point A, 20 metres above the level of water in a lake, the angle of elevation of a cloud is 30^o . The angle of depression of the reflection of the cloud in the lake, at A is 60^o . Find the distance of the cloud from A.

A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60^o with the wall, then find the height of the wall.

A statue 1.46 m tall stand on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60^o and from the same point, the angle of elevation of the top of the pedestal is 45^o . Find the height of the pedestal. \((\sqrt { 3 } =1.73)\) .

From a window (60 metres high above the ground) of a house in street the angles of elevation and depression of the top and the foot of another house on opposite side of street are 60^o and 45^o respectively. Show that the height of the opposite house is \(60(1+\sqrt { 3 } )\) metres.

An aeroplane is at an altitude of 1200 m. Find that two ships are sailing towards it in the same direction. The angles of depression of the ships as observed from the aeroplane are \(60°\) and \(30°\) , respectively. Find the distance between both ships.

The top of a broken tree has its top touching the ground (shown in the following figure) at a distance of 10 m from the bottom. If the angle made by the broken part with ground is 30°, then find the length of the broken part.

A boy standing on a horizontal plane finds a bird flying at a distance of 100 m from him at an elevation of 30^o. A girl standing on the roof of 20 metre high building, finds the angle of elevation of the same bird to be 45^o. Both the boy and the girl are on opposite sides of the bird. Find the distance of bird from the girl. [given \(\sqrt2\) = 1414]

From the top of a building 60 m high, the angles of depression of the top and bottom of a vertical lamp post are observed to be 30^o and 60^o respectively. Find
(i) The horizontal distance between the building and the lamp post.
(ii) The height of the lamp post, \(\sqrt { 3 } =1.732\).

A bird is sitting on the top of a tree, which is 80 m high. The angle of elevation of the bird, from a point on the ground is 45^o . The bird flies away from the point of observation horizontally and remains at a constant height. After 2 seconds, the angle of elevation of the bird from the point of observation becomes 30^o . Find the speed of flying of the bird.