Height And Distance Class 10 Important Questions Pdf Download UPDATED
Paula Yacovone
Other attributes were taken out for clarity, but I think the issue lies with scaling the height to 100% in nested containers like how you are trying to scale height in your nested containers. The parent classes height will need to be applied the 100%. - What i'm curious about is why fixed: position corrects the scale and fails without it; this is something i'll learn eventually with some more practice.
Question 4.
The angles of depression of the top and bottom of a 50 m high building from the top of a tower are 45 and 60 respectively. Find the height of the tower and the horizontal distance between the tower and the building,
Solution:
Question 5.
A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60 and the angle of depression of the base of hill as 30. Find the distance of the hill from the ship and the height of the hill.
Solution:
Question 8.
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 and 45 respectively. Find the vertical distance between the aeroplanes at that instant
Solution:
Question 10.
The angles 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.
Solution:
Question 11.
The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60. From a point Y, 40 m vertically above X, the angle of elevation of the top Q of tower is 45. Find the height of the tower PQ and the distance PX.
Solution:
Question 13.
From a point on the ground, the angle of elevation of the top of a tower is observed to be 60. From a point 40 m vertically above the first point of observation, the angle of elevation of the top of the tower is 30. Find the height of the tower and its horizontal distance from the point of observation.
Solution:
Question 23.
Two poles of equal heights are standing opposite to each other on either side of the road which is 80 m wide. From a point P between them on the road, the angle of elevation of the top of a pole is 60 and the angle of depression from the top of another pole at point P is 30. Find the heights of the poles and the distance of the point P from the poles.
Solution:
Question 24.
Two ships are there in the sea on either side of a light house in such a way that the ships and the light house are in the same straight line. The angles of depression of two ships as observed from the top of the light house are 60 and 45. If the height of the light house is 200 m, find the distance between the two ships.
Solution:
Question 26.
Two ships are approaching a lighthouse from opposite directions. The angles of depression of the two ships from the top of the lighthouse are 30 and 45. If the distance between the two ships is 100 m, find the height of the lighthouse
Solution:
Question 27.
The angles of elevation and depression of the top and the bottom of a tower from the top of a building, 60 m high, are 30 and 60 respectively. Find the difference between the heights of the building and the tower and the distance between them
Solution:
Question 29.
The angle of elevation of the top of a tower at a distance of 120 m from a point A on the ground is 45. If the angle of elevation of the top of a flagstaff fixed at the top of the tower, at A is 60, then find the height of the flagstaff.
Solution:
Question 31.
The horizontal distance between two poles is 15 m. The angle of depression of the top of first pole as seen from the top of second pole is 30. If the height of the second pole is 24 m, find the height of the first pole
Solution:
Question 33.
The angles of elevation of the top of a tower from two points at a distance of 6 m and 13.5 m from the base of the tower and in the same straight line with it are complementary. Find the height of the tower.
Solution:
Question 36.
Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60 and 30 respectively. Find the height of the poles and the distances of the point from the poles.
Solution:
Question 43.
The angle of depression from the top of a tower of a point A on the ground is 30. On moving a distance of 20 m from the point A towards the foot of the tower to a point B, the angle of elevation of the top of the tower from the point B is 60. Find the height of the tower and its distance from the point A.
Solution:
Question 60.
A man on the deck of a ship, 12 m above water level, observes that the angle of elevation of the top of a cliff is 60 and the angle of depression of the base of the cliff is 30. Find the distance of the cliff from the ship and the height of the cliff.
Solution:
Question 42.
The angle of elevation of the top of a vertical tower PQ from a point X on the ground is 60. From a point Y, 40 m vertically above X, the angle of elevation of the top Q of tower is 45. Find the height of the tower PQ and the distance PX. (Use \(\sqrt3\) = 1.732) (2016 OD)
Solution:
Let QR = x m
Hence, height of the tower PQ is 96.54 m and the distance PX is 109.3 m.
9. An aero plane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 300 and 600 respectively. Find the distance between the two planes at that instant.
Two points A and B are on the same side of a tower and in the same straight line with its base. The angles of depression of these points from the top of the tower are 60 and 45 respectively. If the height of the tower is 15 m, then find the distance between the points.
The angle of elevation of the top of a tower as observed form a point in a horizontal plane through the foot of the tower is 32. When the observer moves towards the tower a distance of 100 m, he finds the angle of elevation of the top to be 63. Find the height of the tower and the distance of the first position from the tower. [Take tan 32 = 0.6248 and tan 63 = 1.9626]
The angle of elevation of the top of a tower from a point A on the ground is 30. On moving a distance of 20 metres towards the foot of the tower to a point B the angle of elevation increases to 60. Find the height of the tower and the distance of the tower from the point A.
From the top of a building 15 m high the angle of elevation of the top of a tower is found to be 30. From the bottom of the same building, the angle of elevation of the top of the tower is found to be 60. Find the height of the tower and the distance between the tower and building.
The angles of depression of the top and bottom of 8 m tall building from the top of a multistoried building are 30 and 45 respectively. Find the height of the multistoried building and the distance between the two buildings.
Two boats approach a light house in mid-sea from opposite directions. The angles of elevation of the top of the light house from two boats are 30 and 45 respectively. If the distance between two boats is 100 m, find the height of the light house.
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 the second pole is 30. If the height of the second pole is 24 m, find the height of the first pole. 3=1.732 [CBSE 2013]
The angles 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 complementary. Prove that the height of the tower is 6m.
From the top of a building AB, 60 m high, the angles of depression of the top and bottom of a vertical lamp post CD are observed to be 30 and 60 respectively. Find
(i) the horizontal distance between AB and CD
(ii) the height of the lamp post.
(iii) the difference between the heights of the building and the lamp post.
From the top of a light house, the angles of depression of two ships on the opposite sides of it are observed to be α and β. If the height of the light house be h metres and the line joining the ships passes through the foot of the light house, show that the distance between the ship is
h tan α +tan β tan α +tan β metres.
If the angles 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 in the same straight line with it are complementary, find the height of the tower.
Question 1.
A man standing on the deck of a ship, which is 10 m above the water level, observes the angle of elevation of the top of a hill as 60 and the angle of depression of the base of the hill as 30. Calculate the distance of the hill from the ship and the height of the hill.
Solution:
In Fig. 11.54, let C represents the position of the man on the deck of the ship, A represents the top of hill and D its base.
Now in right-angled triangle CWD,
Now, AD = AB + BD = 30 m + 10 m = 40 m.
Therefore, the distance of the hill from the ship = 17.3 m and the height of the hill = 40 m