Two walls of equal height are on either side of a road, which is 100 m wide. At a point on the road two stairs are along the two walls in such a way that they indicate the two angles of elevation from that point at 60° and 30°. The length of the longer stair is:

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 pole 10 m long rests slantly against a vertical wall AB making an angle 30° with the horizontal (ground). Find how far the foot of the pole is from the wall (in metres).

If a ladder leans against a wall at a height of 2.732m and its foot rests on the ground making an angle of 75°, find the length of the ladder.(3^1/2 = 1.732 , 2^1/2 = 1.414)

From a lighthouse of height 3√3 m, the angle of depressions of two ships A and B coming from opposite sides are 30° and 60° respectively. If there is a mirror in ship B, what is the distance between ship A and its image in the mirror?

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?

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?

For a bird flying at a height of 10√3 m, the angle of depression to the top of a tree and the bottom of the tree at a particular moment is 30° and 45° respectively. What is the height of the tree (in m)? (Take √3 = 1.732)

A building of height 2√3 m is observed from two points A and B, point B being 1 m further from the building than point A. If the angles of elevations from A and B are complementary angles, find the distance of point B from the building.

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).

From a point A, a flight is flying 100√3 m above the ground is observed at two time instants. The angle of elevation at different times are 60° and 30° respectively. If the time taken by the flight to move from those two points is 5 seconds, what will be the time taken by the flight to cover 360 km?

A boy stands at 12√3 feet from the foot of a hill of height 17 feet. The angle of elevation to the hill from the head of the boy is 30º. Find the height of the boy.

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.

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.

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

For a bird flying at a height of 10√3 m, the angle of depression to the top of a tree and the bottom of the tree at a particular moment is 30° and 45° respectively. What is the height of the tree (in m)? (Take √3 = 1.732)

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? 

Two ships C and D move towards a lighthouse from the opposite sides. The angle of elevation of the top of the lighthouse from ships C and D are 60° and 30°. If C and D are 200 m away, then what is the height of the lighthouse? (in m)

An observer 1.5 m tall is 24.5 m away from a 26 m high tower. The angle of elevation of the top of the tower from the eye of the observer is:

An observer 1.5 m tall is standing 28.5 m away at the same level as the foot of a tower. If the angle of elevation of the observer watching the top of the tower is 45°, then what is the height of the tower?

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?

The angle of elevation of a Parachute flying from a point on the ground is 60. After flying for 2 hours 28 minutes the elevation angle reduces to 30. If the Parachute is flying horizontally at a constant height of 2450 m, find the speed of the Parachute if it is moving at a uniform speed.

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? 

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?

From a lighthouse of height 3√3 m, the angle of depressions of two ships A and B coming from opposite sides are 30° and 60° respectively. If there is a mirror in ship B, what is the distance between ship A and its image in the mirror?

A boy stands at 12√3 feet from the foot of a hill of height 17 feet. The angle of elevation to the hill from the head of the boy is 30º. Find the height of the boy.

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 ship during the period of observation is:

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).

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?

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.