Two ships are on the opposite of a light house such that all three of them are collinear. The angles of depression of the two ships from the top of the light house are 30° and 60°. If the ships are 230√3 m apart, then find the height of the light house (in m).

Two pillars of equal height stand on either side of a roadway which is 150 m wide. At a point in the road between pillars, the elevations of the pillars are x^o and y^o that \(\tan x^\circ = \frac{2}{5}, \tan y^\circ = \frac{3}{5}\), then the height of each pillar is:

The angle of elevation of the top of a building at a distance of 70 m from its foot on a horizontal plane is found to be 60°. Find the height of the building

From the top of an upright pole 17.75 m high, the angle of elevation of the top of an upright tower was 60⁰. If the tower was 57.75 m tall, how far away (in m) from the foot of the pole was the foot of the tower?

The angle of elevation of the top of a tower from the top of a building whose height is 680 m is 45° and the angle of elevation of the top of the same tower from the foot of the same building is 60°. What is the height (in m) of the tower? 

From the top of an upright pole 24√3 feet high, the angle of elevation of the top of an upright tower was 60°. If the foot of the pole was 60 feet away from the foot of the tower, what tall (in feet) was the tower? 

From the top of a tower, the angle of depression of the top of a 10 m high building is 60^o. If the distance between the tower and the building is \(50\sqrt{3}\) m, find the height of the tower.

The shadow of a tower on the ground level is increased by 30 m, when the angle of depression by the sun changes from 60^o to 30^o. The height of the tower is?

The height of a lighthouse is 20 meters above sea level. The angle of depression (from the top of the lighthouse) of a ship in the sea is 30^o. What is the distance between the ship from the foot of the lighthouse?

The angle of elevation of the top of a tower at a distance of 25 m from its foot is 60^o. The approximate height of the tower is -

A man observed the top of an electric pole at angles of elevation of 60° and 30°, respectively, from two different observation points P and Q. If the distance between P and Q is 10 m, find the height of the pole (in m).

The shadow of a tower standing on level ground is found to be 40 m longer when the Sun's altitude is 30° than when it was 45°. Find the height (in meters) of the tower.

A pole stands vertically on the ground with the help of a 12-metre steel wire tied to its top and affixed on the ground. If the steel wire makes an angle of 30° with the horizontal ground, then the height of the pole is equal to:

A person standing at a distance looks at a building having a height of 1000 metres. The angle between the top of the building and the ground is 30°. At what approximate distance (in metres) is the person standing away from the building.

A vertical pole of 28 m in height casts a 19.2 m long shadow. At the same time, find the length of the shadow cast by another pole of 52.5 m in height.

Angle of elevation of a building from a point 20 m away from the base of tree is 30°. Find the height of building.

From a point P, the angle of elevation of a tower is such that its tangent is 3/4. On walking 490 metres towards the tower the tangent of the angle of the tower becomes 4/3. What is the height (in metres) of the tower?

An airplane is flying at a constant height 'h'. At 10:00 am, it appears at an elevation angle of 30°. After 1 min, it appears at an elevation angle of 60°. If the speed of the airplane is 960 km/h, find the value of 'h'. (height upto two decimal )

Two poles of heights 10 m and 15 m are 25 m apart. What is the height of the point of intersection of the lines joining the tip of each pole to the foot of the other pole?

A and B are two points on the same side of a tree, 50 metres apart. The angles of elevation of these points to the top of a tree are 60° and 30°, respectively. What is 40% of the height of the tree (in m)

A poster is on top of a building. A person is standing on the ground at a distance of 50 m from the building. The angles of elevation to the top of the poster and the bottom of the poster are 45° and 30°, respectively. What is 200% of the height (in m) of the poster

Exactly midway between the foot of two towers P and Q, the angles of elevation of their tops are 45° and 60°, respectively. The ratio of the heights of P and Q is:

A poster is on top of a building. A person is standing on the ground at a distance of 50m from the building. The angles of elevation to the top of the poster and bottom of the poster are 45° and 30°, respectively. What is 200% of the height (in m) of the poster?

A vertical pole and a vertical tower are on the same level ground in such a way that, from the top of the pole, the angle of elevation of the top of the tower is 60° and the angle of depression of the bottom of the tower is 30°. If the height of the pole is 24 m. then find the height of the tower (in m).

A building of height 100√3 m is illuminated by the sun at an angle of 60°. A person P is at a distance of 200 m further than the tip of the shadow of the building. What is the angle of elevation of the top of the building for person P?

Ram is standing at the foot of a building while Ramesh is standing at the top of the same building. A crow is flying at a distance of 20 m from Ram. The angle of elevation made by the crow with respect to Ram is 30°, while the angle of depression made by the crow with respect to Ramesh is 60°. What is the height of the building?

The angle of elevation of the top of an unfinished tower at a point distant 78 m from its base is 30°. How much higher must the tower be raised (in m) so that the angle of elevation of the top of the finished tower at the same point will be 60°?

Two pillars of equal height stand on either side of a roadway, which is 150 m wide. At a point in the road between pillars, the elevation angles of the pillars are x° and y°, where tan x° = 2/5, tan y° = 3/5 , then the height of pillar is:

The angle of elevation of the top of a tree from a point on the ground which is 300m away from the tree is 30°. When tree grew up, its angle of elevation of the top of it became 60° from the same point. How much did the tree grow? (nearest to an integer)

A balloon is directly above a point A and rises vertically at a constant rate of 3 m/s. An observer at point B, which is 400 m horizontally from A, observes the balloon. At the moment when the angle of elevation is 45°, how long will it take for the angle to become 60°, assuming no horizontal drift?

The angle of depression from a lighthouse on two boats is 30° and 60°. The boats are traveling from the same side and the height of the lighthouse is 62√3 meters. Find the distance between the two boats.

A building of height 'h' is observed from a point in mid-air at a perpendicular distance of 3 m from the building. If the angle of elevation at the top of the building and the angle of depression at the bottom of the building is 45° and 30°, what is the value of h?

In the figure given below, two birds A and B are at different heights. An eagle is at higher altitude but along the horizontally at the midpoint of the birds (i.e. Horizontal distance of bird A and eagle is same the horizontal distance between bird B and eagle). The angles of elevation of eagle and bird A from bird B are 60° and 30° respectively and the distance between the birds is 10 m. What is the difference of altitudes at which eagle and bird A are flying? (in m)

An aeroplane flies at a constant horizontal height of 100 m. For an observer standing on the ground, the angle of elevation changes from 30° to 45° in 1.22 seconds. What is the speed (in km/hr) of the aeroplane? (Use √3 = 1.732)

A ladder is leaning against a 3 m high wall. It makes an angle of 60° with the ground. If another ladder is placed on the opposite side of the wall whose length is √3 times the length of the original ladder, then what will be the angle made by that ladder with the ground?

An airplane is flying horizontally at a speed of 144√3 km/hr at some height above the ground. The angle of elevation of the plane from a point X is 30° and after 45 seconds, its angle of elevation from X becomes 60°. What is the vertical height above the ground at which the plane is flying?

A balloon is directly above a point A and rises vertically at a constant rate of 3 m/s. An observer at point B, which is 400 m horizontally from A, observes the balloon. At the moment when the angle of elevation is 45°, how long will it take for the angle to become 60°, assuming no horizontal drift?

A building of height 100√3 m is illuminated by the sun at an angle of 60°. A person P is at a distance of 200 m further than the tip of the shadow of the building. What is the angle of elevation of the top of the building for person P?

A poster is on top of a building. A person is standing on the ground at a distance of 50m from the building. The angles of elevation to the top of the poster and bottom of the poster are 45° and 30°, respectively. What is 200% of the height (in m) of the poster?

Exactly midway between the foot of two towers P and Q, the angles of elevation of their tops are 45° and 60°, respectively. The ratio of the heights of P and Q is:
(CGL 2021 Pre)
 

The angle of elevation of the top of an unfinished tower at a point distant 78 m from its base is 30°. How much higher must the tower be raised (in m) so that the angle of elevation of the top of the finished tower at the same point will be 60°?

The angle of elevation of the top of a tree from a point on the ground which is 300m away from the tree is 30°. When tree grew up, its angle of elevation of the top of it became 60° from the same point. How much did the tree grow? (nearest to an integer)

A vertical pole and a vertical tower are on the same level ground in such a way that, from the top of the pole, the angle of elevation of the top of the tower is 60° and the angle of depression of the bottom of the tower is 30°. If the height of the pole is 24 m. then find the height of the tower (in m).

Two ships are in opposite directions from a lighthouse such that all three are in a straight line. The angles of depression of the two ships from the top of the lighthouse are 30° and 60°. If the distance between the ships is 230√3 m, find the height of the lighthouse (in meters).

From the top of an upright pole 17.75 m high, the angle of elevation of the top of an upright tower was 60⁰. If the tower was 57.75 m tall, how far away (in m) from the foot of the pole was the foot of the tower?

The angle of elevation of the top of a tower from the top of a building whose height is 680 m is 45° and the angle of elevation of the top of the same tower from the foot of the same building is 60°. What is the height (in m) of the tower? 

As observed from the top of a lighthouse, 42 m high above sea-level, the angle of depression of a ship sailing directly towards it changes from 30° to 45°. The distance travelled by the ship during the period of observation is:

A vertical pole and a vertical tower are on the same level of ground in such a way that from the top of the pole, the angle of elevation of the top of the tower is 60° and the angle of depression of the bottom of the tower is 30°. If the height of the tower is 76 m, then find the height (in m) of the pole.

A and B are standing on the same side of a wall and observe that the angles of elevation to the top of the wall are 45° and 60° respectively. If the height of the wall is 50 m. The distance between A and B is: (Use \(\sqrt3 \)= 1.73 and \(\sqrt2\) = 1.41)

Two ships are sailing in the sea on two sides of a lighthouse. The angles of elevation of the top of the lighthouse as observed from the two ships are 30° and 45° respectively. If the lighthouse is 90 m high, then the distance between the two ships is ______.