Two points A and B are on the ground and on opposite sides of a tower. A is closer to the foot of tower by 42m than B. If the angles of elevation of the top of the tower, as observed from A and B. are 60°and 45° respectively, then the height of the tower is closest to:

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 ______.

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 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)

A vertical pole of length 60 m is situated on the horizontal plane. The base of the pole is at P. There are two points, A and B, such that P, A, and B are on the same straight line. Let the angles of elevation of the top of the pole from A and B be α & β (α > β) respectively. If PA = 48 m and AB = 27 m, then what is α + β equal to?

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?

A flag pole on the top of a mall building is 75 m high. To an observer at a height of 400 m, the mall building and the pole subtend an equal angle θ. If the height of the mall building is 325 m. Then find the horizontal distance (in m) of the observer from the pole.

A vertical tower standing at the corner of a rectangular field subtends angles of 60° and 45° at the two nearer corners. If θ is the angle that the tower subtends at the farthest corner, then what is cotθ equal to?

A mirror is placed on the ground facing upwards. A man sees the top of a tower in the mirror which is at a distance of 105 m from the mirror. The man is 0.5 m away from the mirror, and his height is 1.5 m. Find the height of the tower (in metres).

An aeroplane flying horizontally 1 km above the ground is observed at an elevation angle of 60°, and after 10 seconds, the elevation angle from same place is observed to be 30°. Find the uniform speed of the aeroplane in km/h ?

At a point on a horizontal line through the base of a monument, the angle of elevation of the top of the monument is found to be such that its tangent is 1/5 . On walking 138 m towards the monument the secant of the angle of elevation is found to be √193/12. The height of the monument (in meters) is 

A vertical pole of length 80 m is situated on the horizontal plane. The base of the pole is at P. There are two points, A and B, such that P, A, and B are on the same straight line. Let the angles of elevation of the top of the pole from A and B be α & β (α>β), respectively. If PA = 64m and AB = 36 m, then what is α + β equal to:

If the angle of elevation of a cloud from a point P, 25 m above a lake, is 30°, and the angle of depression of the reflection of the cloud in the lake from P is 60°. Find the height of the cloud above the surface of the lake?

There are two temples, one on each bank of the river just opposite to each other. One temple is 54 m high. From the top of this temple, the angles of depression of the top and the foot of the other temple is 30° & 60° respectively. The length of the temple is?

A flagpole on the top of a mall building is 75 m high. To an observer at a height of 400 m, the mall building and the pole subtend an equal angle θ. If the height of the mall building is 325 m. Then find the horizontal distance (in m) of the observer from the pole.

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 60º and the angle of depression of the bottom of the tower is 30º. If the height of the pole is 24m, then find the height of the tower (in m).

Let A and B be two towers with the same base. From the midpoint of the line joining their feet, the angles of elevation of the tops of A and B are 30° and 45°, respectively. The ratio of the heights of A and B is :

Two pillars A and B of the same height are on opposite sides of a road which is 40 m wide. The angles of elevation of the tops of the pillars A and B are 30º and 45º, respectively, at a point on the road between the pillars. What is the difference (in m) of the point from the foot of pillar A?

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.

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 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 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 ladder of length L is used to climb a wall 15 ft high. If the angle between the ladder and the wall is 30°, find the length of the ladder.

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?

Somewhere in a river is a lighthouse (AB) 15 m high. The angle of elevations from points P and Q, which are on either bank of river, to the top of the lighthouse are 30° and 60° respectively. Points P, Q and B lie in a straight line (B is base of the lighthouse). Find the width of the river.

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?

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 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).

Two points A and B are on the ground and on opposite sides of a tower. A is closer to the foot of tower by 42m than B. If the angles of elevation of the top of the tower, as observed from A and B. are 60°and 45° respectively, then the height of the tower is closest to:

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 vertical lamp-posts of equal height are on either side of a road 50 m wide. At a point on the road between the lamp-posts, the elevations of the tops of lamp-posts are 60° and 30°. Find the height of the lamp-post.

Points P and Q are on the opposite sides of a tower. The angle of elevation of the top of the tower from points P and Q are 60° and 30° respectively and the distance between P and Q is 136√3 m. What is the height of the tower (in m)?

The angles of elevation of the top of the tower from two points on the ground at a distance of 18 m and 32 m from the foot of the tower are complementary. The height of the tower is...

Two vertical lamp-posts of equal height are on either side of a road 50 m wide. At a point on the road between the lamp-posts, the elevations of the tops of lamp-posts are 60° and 30°. Find the height of the lamp-post.

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 angles of elevation of the top of the tower from two points on the ground at a distance of 18 m and 32 m from the foot of the tower are complementary. The height of the tower is...

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:

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:

From the top of a platform 5 m high, the angle of elevation of a tower was 30°. If the tower was 45 m high, how far away from the tower was the platform positioned?

A shadow of a tower standing on a level ground is found to be 40√3 meters longer when the Sun's altitude is 30º than when it is 60. The height of the tower is:

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.

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:

In the following figure, CD is a building that is two-thirds taller than another building AB, which is 30√3 m away from it. If the angle of inclination from the top of building AB to the feet of CD is 60°, what is the value of the angle of declination from the top of building AB to the top of building CD?

A ladder is leaning against a wall of a height of 3m. It makes an angle of 60° with the ground. If the height of the ladder was √3 times the length of the original ladder, what will be the angle made?

Points P and Q are on the opposite sides of a tower. The angle of elevation of the top of the tower from points P and Q are 60° and 30° respectively and the distance between P and Q is 136√3 m. What is the height of the tower (in m)?

The top of two lamp posts of height 20 m and 30 m are connected by a wire. If the wire makes an angle of 30° with the horizontal, then find the length of the wire.

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)

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:

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?