CBSE Class 10 Mathematics Important Questions for Exam 2023 (Chapter - Height and Distance)

 

Important Mathematics Questions of  Class X Chapter {Height and Distance} for CBSE    Examination 2023

 

1)      AB is a 6M high pole and CD is a ladder inclined at an angle of 60° to the horizontal and reaches up to the point D of pole. If AD is equal to 2.54 find the length of the ladder.

2)      A ladder 15m long just reaches the top of a vertical wall if the ladder makes an angle of 60 degree with the wall then find the height of the wall.

3)       If the height and length of the shadow of a man are the same, then find the angle of elevation of the Sun.

4)      Find the length of the shadow on the ground of a pole of height 6M when the angle of elevation P of the sun is such that tanP = ¾.

5)      A ladder leaning against the wall makes an angle of 60 degree with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder.

6)      A kite is flying at a height of 30 M from the ground. The length of string from the ground to the kite is 60 M. assuming that there is no slack in the string, find the angle of elevation of the kite at the ground.

7)      If the angle of elevation of the top of a tower from a distance of 100M from its foot is 60 degree then what will be the height of the tower.

8)      An observer 1.7 M tall is 20√3 M away from a tower.  The angle of elevation from the eye of an observer to the top of a tower is 30 degree. Find the height of the Tower.

9)      A kite is flying at a height of 90 m above the ground, the string attached to the kite is temporary tied to a point on the ground. The inclination of the string with the ground is 60 degree find the length of the string assuming that there is no slack in the string.

10)  A tower stands vertically on the ground from a point on the ground which is 16 away from the foot of the tower the angle of elevation of the top of the tower is found to be a 60 degree.  find the height of the tower.

11)  From a point P on the ground the angle of elevation of the top of a 10 M tall building is 30 degree. A flag is hosted at the top of the building and the angle of elevation of the top of the flagstaff from p is 45 degree. Find the length of the flagstaff and distance of building from point P.

12)  A tree is broken by the wind its top struck the ground at an angle of 60° and at a speed of 30 M from the root of the tree. Find the whole height of the tree.

13)  An observer 1.5 m tall is 20.5 m away from a tower 22m high.  Determine the angle of elevation of the top of the tower from the eye of the observer.

14)  Two men on either side of a 75 M high building and in a line with base of building observe the angle of elevation of the top of the building as 30 degree and 60 degree. Find the distance between the two men.

15)  A 7 M long flagstaff is fixed on the top of a tower standing on the horizontal plane. From a point on the ground the angles of elevation of the top and bottom of the flagstaff are 60 degree and 45 degree respectively find the height of the tower correct to one place of decimal.

16)  An Aeroplane when flying at a height of 4000 m from the ground passes vertically above another aeroplane at an instant when the angles of elevation of the two planes from the same point on the ground are 60 degree and 45 degree respectively. Find the vertical distance between aeroplanes at that instant.

17)  A man standing on the Deck of a ship which is 10 m above water level observe the angle of elevation of the top of a hill at 60 degree and the angle of depression of the base of the hill as 30 degree find the distance of the hill from the ship and the height of the hill.

18)  Two ships are approaching a lighthouse from opposite directions. The angle of depression of Two Ships from top of the light house are 30° and 45° if the distance between two Ships is 100 m find the height of the Lighthouse.

19)  The angle of depression of the top and bottom of an 8m. Tall building from top of a multi storey building are 30 degree and 45 degree respectively. Find the height of multi storied building and distance between two buildings.

20)  Two poles of equal Heights are standing opposite to each other on either side of a road, which is 80 m wide from a point between them on the road angles of elevation of the top or 30 degree and 60 degree. Find the height of the poles and distance of point from poles.

21)  A bird is sitting on the top of 80 M high tree.  From a point on the ground the angle of elevation of the bird is 45 degree. The bird flies away horizontally in such a way that it remained at a constant height from the ground. After 2 seconds the angle of elevation of the bird from the same point is 30°. Find the speed of flying of the bird.

22)  The angle of elevation of an Aeroplane from a point on the ground is 60 degree. After a flight of 30 seconds the angle of elevation changes to 30°. If the plane is flying at a constant height of 3600√3 meter. Find the speed of the plane in kilometer per hour.

23)  A man on the top of a vertical Tower observes a car moving at a uniform speed towards him if it takes 12 minutes for the angle of depression to change from 30 degree to 45 degree, how soon after this, the car will reach the tower?

24)  A pole has to be erected at a point on the boundary of a circular Park of diameter of 13 M is such a way that the differences of its distance from two opposite fixed gates A and B on the boundary is 7.  Is it possible to do so? If so, at what distance from the pole it is to be erected?

25)  The angle of elevation of the top of a Chimney from the foot of a tower is 60 degree and the angle of depression of the foot of the chimney from the top of the tower is 30°. If the height of the Tower is 40m. Find the height of the smoke emitting Chimney according to pollution control norms. The minimum height of the smoke editing Chimney should be 100m. What value is discussed in this question?

26)  A straight highway leads to the foot of a tower. A man standing at the top of the tower observed at an angle of depression of 30 degree, which is approaching the foot of the tower with a uniform speed.  6 second later the angle of depression of the car is found to be 60 degree.  find the time taken by the car to reach the foot of the tower from this point.

27)  From the top of a building 60 M high the angle of depression of the top and bottom of a tower are observed to be 30 degree and 60 degree. Then find the height of the tower.

28)  The angle of elevation p of the top of a Lighthouse as seen by a person on the ground is such that tan p = 5/12. When the person moves a distance of 240 towards the Lighthouse the angle of elevation becomes q such that tan q = ¾.  Find the height of the Lighthouse.

30)  The horizontal distance between two poles is 15 m the angle of depression of the top of the first pole as seen from the top of second Pole is 30 degree. If the height of the second Pole is 24m, find the height of the first pole.

31)  The angle of elevation of an aeroplane from a point on the ground is 45 degree. After flying for 15 seconds the angle of elevation changes to 30 degree. If the aeroplane is flying at a constant height of 2500 m, then find the average speed of the aeroplane.

32)  A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30 degree with it. The distance between the foot of the tree to the point where the top touches the ground is 8m. Find the height of the tree.

33)  The angle of elevation of the top of a tower from a point on the ground, which is 30 M away from the foot of the tower, is 30 degree. Find the height of the tower.

34)  A kite is flying at a height of 60 m above the ground. The string attached to the archive is temporarily tied to a point on the ground. The inclination of the string with the ground is 60 degree. Find the length of the string assuming that there is no slack in the string.

35)  From a point on the ground, the angle of elevation of the bottom and the top of a transmission Tower fixed at the top of 20 High Building are 45 degree and 60 degree respectively. Find the height of the tower.

36)  A statue 1.6 M tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue A 60 degree and from the same point the angle of elevation of the top of the pedestal is 45 degree. Find the height of the pedestal.

37)  The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of a building is 60 degree. If the Tower is 50 M high, find the height of the building.

38)  A window in a building is at a height of 10 m from the ground. The angle of depression of a point P on the ground from the window is 30 degree. The angle of elevation of the top of the building from the point P is 60 degree. Find the height of the building.

39)   A vertical Tower stands on a horizontal plane and is surmounted by a flagstaff of height 5m. From a point on the ground the angles of elevation of the top and bottom of the flagstaff are 60° and 30° respectively. Find the height of the tower and the distance of the point from the tower.

40)  The angle of elevation of the top Q of a vertical Tower PQ from a point X on the ground is 60 degree. From a point Y, 40 m vertically above X, the angle of elevation of the top q of Tower is 45 degree. Find the height of the tower PQ and the distance PX.

41)  As observed from the top of a lighthouse, 100 M high above sea level, the angles of depression of a ship, sailing directly towards it, changes from 30 degree to 60 degree. Find the distance travelled by the ship during the period of observation.

42)  From a point on the ground, the angle of elevation of the top of a tower is observed to be 60 degree. from a point 40 m  vertically above the first of observation, the angle of elevation of the top of the Tower is 30°. Find the height of the tower and horizontal distance from the point of observation.

43)  The angle of elevation of the top of a tower from certain point is 30 degree. If the observer moves 20 m towards the tower, the angle of elevation of the top increases by 15 degree. Find the height of Tower.

44)  The angle of elevation of the top of a tower 30 M high from the foot of another tower in the same plane is 60 degree and the angle of elevation of the top of the second Tower from the foot of the first hour is 30 degree. Find the distance between the two Towers and also the height of the other Tower.

45)  The angle of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are 60° and 30° respectively. Find the height of the tower.

46)  From the top of a hill the angles of depression of two consecutive kilometer stones due east are found to be 30 degree and 60 degree. Find the height of the hill.

47)  The angles of depression of the top and bottom of a 50 M high building from the top of a tower are 45 degree and 60 degree respectively. Find the height of the tower and the horizontal distance between the tower and the building.

       48) From a window 15 M high above the ground in a street, the angles of elevation                   and depression of the top and the foot of another house on the opposite side of                 the street are 30° and 45° respectively show  that the height of the opposite                         house is 23.36 Meters.