Some Applicatio...

AB is a vertical pole. The end A is on the level ground and C is the middle point of AB. P is a point on the level ground. The portion BC subtends an angle at P. If AP = nAB, then tan equals

What is the measure of in the given figure?

A 40 m tall building and a tower are standing in front of each other. Angles of elevation to the top of the tower from the top and base of the building are 45° and 60°, respectively. How high is the tower? ()

From the foot of a 50 m tall building, the angle of elevation of the top of a hill is 60° and the angle of elevation of the top of the building from the foot of the hill is 30°. How high is the hill (length DC in the figure)?

The angle of elevation of the top of an unfinished tower at a point of distance 120 m from its base is 45°. How much height of the tower must be increased so that the angle of elevation becomes 60°?

When the elevation of sun changes from 45° to 30°, the shadow of a tower increases by 60 meters. The height of the tower is

If the angle of elevation of a cloud from a height h above the level of water in a lake is and the angle of depression of its image is , then which of the following cannot be the height of the cloud above the level of water in the lake?

In the given figure, AB is the height of a tree. C and D are the two points in a straight line on the ground at b units and a units respectively away from the tree. What is the height of the tree (AB)?

The angle of elevation of a cloud from a point 60 m above a lake is 30^o and from the same point, the angle of depression of its image in the lake is 60^o. The height of the cloud is

The angle of elevation of the top of a vertical tower from a point P on the ground is 60°. At a point Q, 40 m vertically above P, the angle of elevation is 45°. Find the height of the tower.

If two towers of heights h₁ and h₂ subtend angles 30° and 60°, respectively at the mid-point of the line joining their feet, then h₁ : h₂ is

A light house is constructed on a cliff on the bank of a river. Height of the cliff and the light house is 110 m and 70 m, respectively. From the top of the light house, James sees two boats coming towards the bank in a straight line such that both of them make an angle of depression as 30° and 60°, respectively. What is the distance between the two boats?

A 1.6 m tall observer is 45 meters away from a tower. If the angle of elevation from his eye to the top of the tower is 30°, then the height of the tower in meters is
(Take = 1.732)

Two ships are sailing in the sea on the two opposite sides of a light house. The angles of elevation of the top of the light house as observed from the two ships are 60° and 45°, respectively. If the light house is 100 m high, the distance between the two ships is (take = 1.73)

A ladder rests against a vertical wall at an inclination α to the horizontal. Its foot is pulled away from the wall through a distance p, such that its upper end slides a distance q down the wall and then the ladder makes an angle β to the horizontal.
What is the value of ?

A 50 m high pole stands on a 250 m high building. To an observer at a height of 300 m, the building and the pole subtend equal angles. The distance of the observer from the top of the pole is

A man on the top of a tower observes a car moving towards the base of the tower at an angle of depression . Ten minutes later, the angle of depression of the car is found to be . If the tangent of angle is equal to, co-tangent of angle is equal to and the car is moving with a uniform speed, find the total time taken by the car to reach the base of the tower.

From a point on a horizontal plane, the elevation of the top of a hill is 45°. Now, at an elevation of 15°, he again starts walking 500 m towards its summit where he has the elevation of 75° towards the hill's summit. Then the height of the hill will be

The upper three-quarters of a vertical pole subtend an angle tan^-1(3/5) at a point in the horizontal plane through its foot at a distance of 40 m from it. What is the height of the pole?

An aeroplane flying horizontally 1 km above the ground is observed at an elevation of 60°. If after 10 seconds, the elevation is observed to be 30°, then the uniform speed of the aeroplane is