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

If the height of a tower and the distance of the point of observation from its foot, both are increased by 10% then the angle of elevation of its top remains.........

The height of a tower is 10m.The height of its shadow when sun's altitude 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...........

If the ratio of the length of a pole and its shadow is 1 : 1, then angle of elevation of the sun is.......... .

The angle of ....... of an object viewed, is the angle formed by the line of sight with the horizontal when it is above the horizontal level.

The angle of ....... of an object viewed, is the angle formed by the line of sight with horizontal when it is below the horizontal level.

If the angle of elevation of the top of a tower from two points distance and t from its foot are complementary, the height of the tower is ........

If the ratio of the length of a pole and its shadow is \(\sqrt{3}:1\), then the sun's elevation is ........

If the length of the shadow of a tower is increasing, then the angle of elevation of the sun is .......

The height of an object or distance between two distinct objects can be determined with help of trigonometric ratios.

Trigonometric ratios are same for the same angles.

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 the ratio of the height of a tower and the length of its shadow \(\sqrt{3}:1\), then the elevation of the sun is 30⁰

A tree is broken by the wind, the top struck the ground at an angles of 60⁰ and at a distance of 30m from the root of the tree.Then whole height of the tree is \(30(2+\sqrt{3})m\).

A vertical stick 10m casts a shadow 8m long.At the same time a tower casts a shadow 32m long.Then the height of the tower is

A girl of height 100cm stands in front of lamppost and cast a shadow of length \(100\sqrt{3}\)cm on the ground.The angle of elevation of the top of the lamppost is 

A player sitting on the top of a tower of height 40m observes the angle of depression of a ball lying on the ground as 60⁰.The distance between the foot of the tower and ball is

A tower is 50m high.Its shadow is x metres shorter, when the sun's altitude is 45⁰ than when it is 30⁰, then x=

The angle of depression of the top of a tower at a point 100m from the house is 45⁰ , then the height of the tower is

A tower stands vertically on the ground. From a point on the ground which is 25m away from the foot of the tower, the angle of elevation of the top of the tower is found to be \({ 45 }^{ \circ }\). Then, find the height (in metres) of the tower.

A tree is broken by the wind. The top struck the ground at an angle of  \({ 45 }^{ \circ }\)and it a distance 35m from the foot. Then the whole height of the tree before broken.

The height of a tower is 30 m. Calculate the length of its shadow made on the level ground when the sun's altitude is 60^o . 

If the angle of depression of an object from a 75 m high tower is 30^o, then find the distance of the object from the base of the tower.

If the ratio of height of a tower and the length of its shadow on the ground is \(\sqrt { 3 } :1\), then find the angle of elevation of the sun.

A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30\(\unicode{xb0} \) to 60\(\unicode{xb0} \) as he walks towards the building. Find the distance he walked towards the building.

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.

From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60^o and the angle of depression of its foot is 45^o. Determine the height of the tower.

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. \((\sqrt { 3 } =1.73)\) .

On a horizontal plane there is a vertical tower with a flag pole on the top of the tower. At a point 9 metres away from the foot of the tower the angles of elevation of the top and bottom of the flag pole are 60^o and 30^o respectively. Find the heights of the tower and flag pole mounted on it.

The shadow of a flagstaff is three times as long as the shadow of the flagstaff when the sunrays meet the ground at an angle of 60^o . Find the angle between the sunrays and the ground at the time of longer shadow.

The angle of elevation of a jet fighter from a point A on the ground is 60^o . After a flight of 15 seconds, the angle of elevation changes to 30^o. If the jet is flying at a speed of 720 km/hr, find the constant height. \((\sqrt { 3 } =1.732)\) ^.

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, \(\sqrt { 3 } =1.732\).