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The angle of elevation of the top Q of a...

The angle of elevation of the top Q of a vertical tower PQ from a point X and the ground is `60^(@)`. From a point Y, 40m vertically above X, the angle of elevation of the top Q of the tower is `45^(@)`. Find the height of the tower PQ and the distance PX. (use `sqrt(3)` = 1.73).

Text Solution

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The correct Answer is:
54.6 m
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A TV tower stands verically on the bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60^(@) . From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30^(@) . Find the height of the tower and the width of the canal.

A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60^(@) . From another point 20m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30^(@) (see Figure ). Find the height of the tower and the width of the canal.

Knowledge Check

  • The angle of elevation of the top of a tower from a point of the ground, which is 30 m away from the foot of a tower of height 10sqrt3 , is:

    A
    `45^(@)`
    B
    `60^(@)`
    C
    `30^(@)`
    D
    `90^(@)`

  • If the angle of elevation of the top of a tower from a distance of 100m from its foot is 60^(@) , the height of the tower is

    A
    `100sqrt(3) m`
    B
    `(100)/sqrt(3)` m
    C
    `50sqrt(3) m`
    D
    `(200)/sqrt(3)` m

  • The angle of elevation of the top of a hill from the foot of a tower is 60^(@) and the angle of elevation of the top of the tower from the foot of the hill is 30^(@) . If the height of the tower is 50 m, what is the height of the hill?

    A
    180 m
    B
    150 m
    C
    100 m
    D
    120 m

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    The angle of elevation of the top of a tower from a point O on the ground, qhich is 450 m away from the foot of the tower, is 40^(@) . Find the height of the tower.

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