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Note on Heights and Distances

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One of the main uses of trigonometry is to find the height of an object or the distance between two points. The instruments called theodolite and sextant are used to measure certain angles and then the method of solution of triangles is used to find the required height or distance.

Angle of elevation

Angle of elevation

In the adjoining figure, O is the position of the observer, P is the position of the object and OP is the line of vision. OA is the horizontally through the observation point O. the angle AOP formed when the observer observes the object at P above horizontal line is called an angle of elevation.

Angle of depression

angle of depression

In the adjoining figure, O is the position of the observer, is the position of the object and P is the line of vision.

OP is the horizontal line through the observation point. The angle AOP formed when the observer observes the object at P below the horizontal line is called angle of depression.

  • Angle of elevation
  • Angle of depression
.

Very Short Questions

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  • The angle of elevation of the top of a tower from a point was observed to be 45(^0) and on walking 60 metre away from that point it was found to be 30(^o) .Find the height of the tower .

    81m


    81. 97m


    71.67m


    81.90m


  • The angle of elevation of the top of the tower from a point was observed to be 45(^o).On walking 30 m away from that point was found to be 30(^o) . Find the height of the tower .

    0m


    40 m


    40.98 m


    59.88m


  • The angle of elevation of the top of a point on the ground was observed to be 60(^o) .  On walking 60 m away from that point it was found to be 30(^o) . If the house and these points are in the same line of the same plain , find the height of the house .

    90(sqrt{9})


    30(sqrt{3})


    20(sqrt{2})


    100(sqrt{10})


  • A pole is surrounded on its top by a flagstaff . The angles of elevation of the top and the bottom of the flagstaff as observed from a point 30 metres away from the top of the pole are found to be 45(^o)and 30(^o) respectively . Find the height of the flagstaff .

    12.69 m


    11.667 m


    12.68 m


    12.68 Km


  • A flag of height 7 metres stands on the top of a tower . The angles subtended by the tower and the flagstaff to a point on the gorund are 45o and 15o respectively . Find the height of the tower.

    10.11 m


    12.68 m


    11.11 m


    9.56 m


  • The angle of elevation observed from a place to the roof of house standing infront of the place and to a window 6 m below its roof are found to be  45o and 30o respectively . Find the height of the house .

    14.196 m


    14.116 m


    16.197 m


    15.116 m


  • A pillar is 20 m high . The angle of elevation of the top of a house just infront of it , from the top pillar is 30o and from the foot is 45o.
    Find the distance between the pillar & the house .

    46.77 m


    48. 76 m


    47.32 m


    43. 44 m


  • From the foot of a tree 50 m high , the angle of elevation of a tower is 60o and from the top the angle of elevation is 30o . Find the height of the tower .

    77 m


    78.66 m


    75 m


    70 m


  • A water tank of height 12ft. is fixed on the roof of a building . The angles subtended by the building and the tank to a point on the ground are 45(^o) and 15(^o respectively . Find the height of the building .

    12.56ft


    15.99ft


    13.56ft


    16.93 ft


  • The angle of depression of the top of 70 m high building from the top of a tower is 45(^o) and the angle of elevation of the top of the tower from foot of building is 60(^o. Find the height of the tower .

    45.45m


    98.76m


    95.62 m


    98.34 m


  • The angle of depression of the top of 60 m high building from the tower is 30(^o) If the angle of elevation of the tower from foot of building is 60(^o) , find the height of tower .

    90m


    20m


    70m


    45m


  • From the top of the tower , 80 m high , the measures of the angles of depression of two objects due east of the tower are found to be 45(^o) and 60(^o).Find the distance between the objects.

    76.65m


    33.65m


    58.57m


    33.81m


  • From of the top of tower 100m high the measures of depression of two objects due east of the tower are found to be 45(^o) and 60(^o). Find the distance between the objects.

    42.26m


    23.45m


    46.67m


    78.45m


  • The angles of elevation of the top of tower from two points 242 m and 288 m away from it on the same side a straight line , are found to be complementary. Find the height of tower.

    267 m


    264 m


    462 m


    278 m


  • The angle of elevation of the top of tower from two points 169 m and 196 m away from it on the same side a straight line , are found to be complementary. Find the height of the tower.

    128 m


    187 m


    298m


    182 m


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DISCUSSIONS ABOUT THIS NOTE

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kapil

AB is a straight road leading to C, the foot of a tower. A being at a distance 120 metres from C and B being 75 metres nearer. If the angle of elevation of the tower at B be the double of the angle of elevation of the tower at A, find the height of the tower.


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Rijan

A wooden plank 15m long rest on the wall in such a way that it is at distance of 15÷under root2 from the foot of the ground. Find the angle made on the plank with the ground.


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Aryan

And what about suntended??


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krishna

it is the best and simple way to teach height and distance everyone have to try it


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