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Heights and Distances — NDA Mathematics PYQs

26 previous year questions from Heights and Distances with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

Heights and Distances — NDA Mathematics PYQs

A plane is observed to be approaching the airport. It is at a distance of 10 km from the point of observation and makes an angle of elevation of 67 5^ . What is the height of the p

Consider the following for the two (02) items that follow: The top ( M ) of a tower is observed from three points P , Q and R lying in a horizontal straight line which passes direc

A man at M , standing 100 m away from the base ( P ) of a chimney of height 50 m, observes the angle of elevation of the highest point ( Q ) of the smoke to be 45° . The highest po

Consider the following for the two (02) items that follow: The top ( M ) of a tower is observed from three points P , Q and R lying in a horizontal straight line which passes direc

Paragraph: A flagstaff 20 m long standing on a pillar 10 m high subtends an angle ⁻¹(0.5) at a point P on the ground. Let be the angle subtended by the pillar at this point P . Que

Paragraph: There are two points P and Q due south of a leaning tower, which leans towards north. P is at a distance x and Q is at a distance y from the foot of the tower (x y) . Th

Paragraph: There are two points P and Q due south of a leaning tower, which leans towards north. P is at a distance x and Q is at a distance y from the foot of the tower (x y) . Th

A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h . At a point on the plane the angles of elevation of the bottom and top of the f

Paragraph: There are two points P and Q due south of a leaning tower, which leans towards north. P is at a distance x and Q is at a distance y from the foot of the tower (x y) . Th

A ladder 6 m long reaches a point 6 m below the top of a vertical flagstaff. From the foot of the ladder, the elevation of the top of the flagstaff is 75^ . What is the height of t

The shadow of a tower is found to be x metre longer, when the angle of elevation of the sun changes from 60^ to 45^ . If the height of the tower is 5(3+ 3 ) m , then what is x equa

The angle of elevation of a tower of height h from a point A due South of it is x and from a point B due East of A is y . If AB = z , then which one of the following is correct ?

A ladder 9 m long reaches a point 9 m below the top of a vertical flagstaff. From the foot of the ladder, the elevation of the flagstaff is 60^ . What is the height of the flagstaf

A balloon is directly above one end of a bridge. The angle of depression of the other end of the bridge from the balloon is 48^ . If the height of the balloon above the bridge is 1

The top of a hill observed from the top and bottom of a building of height h is at angles of elevation 6 and 3 respectively. What is the height of the hill?

If a flag-staff of 6 m height placed on the top of a tower throws a shadow of 2 3 ~m along the ground, then what is the angle that the sun makes with the ground?

A spherical balloon of radius r subtends an angle at the eye of an observer, while the angle of elevation of its centre is . What is the height of the centre of the balloon (neglec

The angles of elevation of the top of a tower from the top and foot of a pole are respectively 30^ and 45^ . If h _ T is the height of the tower and h_p is the height of the pole,

From the top of a lighthouse, 100 m high, the angle of depression of a boat is ⁻¹ ( 5 12 ) . What is the distance between the boat and the lighthouse?

A moving boat is observed from the top of a cliff of 150 m height. The angle of depression of the boat changes from 60^ to 45^ in 2 minutes. What is the speed of the boat in metres

Two poles are 10 m and 20 m high. The line joining their tops makes an angle of 15^ with the horizontal. The distance between the poles is approximately equal to

The angles of elevation of the top of a tower standing on a horizontal plane from two points on a line passing through the foot of the tower at distances 49 m and 36 m are 43^ and

The angle of elevation of the top of a tower from a point 20 m away from its base is 45^ . What is the height of the tower?

A lamp post stands on a horizontal plane. From a point situated at a distance 150 m from its foot, the angle of elevation of the top is 30^ . What is the height of the lamp post?

From an aeroplane above a straight road the angles of depression of two positions at a distance 20 m apart on the road are observed to be 30^ and 45^ . The height of the aeroplane

The angles of elevation of the top of a tower from two places situated at distances 21 m and x ~m from the base of the tower are 45^ and 60^ respectively. What is the value of x ?