Practice question on height and distance for IITJEE , AIRFORCE and NDA

height and distance

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Question no. 1

A vertical pole consists of two parts, the lower part being one third of the whole. At a point in the horizontal plane through the base of the pole and distance 20 meters from it, the upper part of the pole subtends an angle whose tangent is 1/2. The possible heights of the pole are

looks_one 20m and 20√3 m

looks_two 20m and 60m

looks_3 16m and 48m

looks_4 None of them

Option looks_two 20m and 60m

Solution :

Question no. 2

From 60 meter high tower angle of depression of the top and bottom of a house are a and b respectively. If the height of the house is (60sin(b-a))/x , then x=

looks_one sin(a) sin(b)

looks_two cos(a) cos(b)

looks_3 sin(a) cos(b)

looks_4 cos(a) sin(b)

Option looks_two cos(a) cos(b)

Solution :

Question no. 3

An observer on the top of the tree, finds the angle of depression of a car moving towards the tree to be 30^o. After 3 minutes this angle becomes 60^o, Alter how much more time, the car will reach the tree

looks_one 4 min

looks_two 4.5 min

looks_3 1.5 min

looks_4 2 min

Option looks_3 1.5 min

Solution :

let the speed of car is x (m / min )
AB = 3 * x = 3x

Question no. 4

A house of height 100 metres subtends a right angle at the window of an opposite house. If the height of the window be 64 m ,then the distance between the two houses

looks_one 48 m

looks_two 36 m

looks_3 54 m

looks_4 72 m

Option looks_one 48 m

Solution :

Question no. 5

The length of the shadow of pole inclined at 10^o to the vertical towards the sun is 2.05 metres , when the elevation of the sun is 38^o . The length of the pole is

looks_one 2.05sin38^o / sin42^o

looks_two 2.05sin42^o / sin38^o

looks_3 2.05cos38^o / cos42^o

looks_4 none of these

option looks_one 2.05sin38^o / sin42^o

Solution :

Draw prependicular from point F on AE
FE = 2.05 m
AF = length of pole
sin38^o = DF/2.05
DF = 2.05sin38^o
sin42^o = DF/AF
AF = DF/sin42^o
AF = 2.05sin38^o/sin42^o

Question no. 6

The horizontal distance between two towers is 60 metres and the angular depression of the top of the first tower as seen from the top of the second, is 30^o. If the height of the second tower be 150 metres , then the height of the first tower is

looks_one 150-60√3 m

looks_two 90 m

looks_3 150-20√3 m

looks_4 none of these

Option looks_3 150-20√3 m

Solution :

Question no. 7

From the top of a light house 60 m high with its base at the sea level, the angle at depression of a boat is 15^o. The distance of the boat from the foot of lighthouse is

looks_one 60(√3-1)/(√3+1) m

looks_two 60(√3+1)/(√3-1) m

looks_3 (√3+1)/(√3-1) m

looks_4 none of these

option looks_two 60(√3+1)/(√3-1) m

Solution :

Question no. 8

An observer in a boat finds that the angle of elevation of a tower standing on the top of cliff is 60^o and that of the top of cliff is 30^o . If height the tower be 60 meters, then the height of the cliff is

looks_one 30 m

looks_two 60√3 m

looks_3 20√3 m

looks_4 none of these

option looks_one 30 m

Solution :

Question no. 9

A tower subtends an angle α at a point A in the plane of its base and the angle of depression of the foot of the tower at a point L meters above A is β . the height of tower is

looks_one L tanβcotα

looks_two L tanβtanα

looks_3 L tanαcotβ

looks_4 L cotαcotβ

Option looks_3 L tanαcotβ

Solution :

Question no. 10

The angle of elevation of a tower from a point A due south of it is 30^o and from a point B due west of it is 45^o, If the height of the tower be 100 m, then AB=

looks_one 150

looks_two 200

looks_3 100√3

looks_4 100√2

Option looks_two 200

Solution :

sin30^o = AC/ AB = 1/2 = 100/AB
AB = 200

Question no. 11

An aeroplane flying horizontally 1 km above the ground is observed at an elevation of 60^o and after 10 seconds the elevation is observed to be 30^o. The uniform speed of the aeroplane in m/sec

looks_one 240

looks_two 240√3

looks_3 60√3

looks_4 none of these

option looks_4 none of these

solution :

let the speed of aeroplane is z
CD = x , DE = y

Question no. 12

From a point "a" metre above a lake the angle of elevation of a cloud is α and the angle of depression of its reflection is β , the height of the cloud is

looks_one a sin (α + β)/sin (α - β)

looks_two a sin (α + β)/sin (β - α)

looks_3 a sin (β - α)/sin (α + β)

looks_4 none of these

Option looks_two a sin (α + β)/sin (β - α)

Solution :

Question no. 13

A balloon is observed simultaneously from three points A,B and C on a straight road directly under it. The angular elevation at B is twice and at C is thrice that of A. If the distance between A and B is 200 m , and the distance between B and C is 100 m, then the height of balloon is

looks_one 50 m

looks_two 50√3m

looks_3 50√2 m

looks_4 none of these

option looks_4 none of these

Solution :

Question no. 14

From an aeroplane vertically over a straight horizontally road , the angle of depression of two consecutive milestones of opposite sides of the aeroplane are observed to be α and β , then the height in miles of aeroplane above the road is

looks_one tanα.tanβ/(cotα+ cotβ)

looks_two (tanα + tanβ)/tanα.tanβ

looks_3 (cotα+ cotβ)/tanα.tanβ

looks_4 tanα.tanβ/(tanα + tanβ)

Option looks_4 tanα.tanβ/(tanα + tanβ)

Solution :

Question no. 15

The angles elevation of a stationary cloud from a point 2500 m above a lake 15^o and the angle depression of its reflection in the lake is 45^o .The height of cloud above the lake level is

looks_one2500√3 m

looks_two 2500 m

looks_3 500√3 m

looks_4 none of these

Option looks_one2500√3 m

Solution :

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