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From a point on the ground, …

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From a point on the ground, the angles of elevation of the bottom and the top of a transmission Tower fixed at the top of a 20 metre high buildings are 45 degree and 65 degree respectively. Find the height of the tower.

    • Posted by Gaurav Pandey 5 years, 3 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Gaurav Seth 5 years, 3 months ago

    Let AB and BC be the tower and water tank and D be the point of observation.
    Given:
    BC = 20m
    ∠BDC = 45° and ∠ADC = 60°
    Let AB = h m
    In ΔBDC
    tan 45° = P/B = BC/DC
    1 = 20/DC [ tan 45°=1]
    DC= 20 m
    Now in ΔADC
    tan 60°= P/B = AC /DC = (AB + BC)/DC
    √3 = (h+20)/20
    20√3 = h+20
    20√3 - 20 = h
    20(√3-1)= h
    h= 20(√3-1) m

    h = 20 (1.73 -1)
    h = 20 × .73 = 14.6 m

    Hence, the height of the tower is 20(√3-1) or 14.6 m.

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