Question

from the lower level ground the angle of elevation is such that the tangents are 5÷12 and if moved 192 m towards the tower that tangents become 3÷5 . then find the height of the tower
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Answer 1

Answer:

Let AB be the tower of height h metres. Let AD=x metres, CD=192 metres.

tanα = , tanβ =

In ∆BAC,

tanα = = ……………………. (i)

In ∆DAB,

tanβ = = or x= ……………………… (ii)

Using (ii) in (i)

=

5= 12h

2880 +20h =36h

16h = 2880 or h= 180

Hence, the height of the tower is 180 metres.

OR

Let AB and CD be two towers of height h m and 60 m respectively.

AC=140m and ÐBDE =300.

In ∆DEB,

tan 30° =

BE == 80.83m

Thus, the height of the first tower is

AB= AE+BE = CD+BE =60+80.83 = 140.83m

Explanation:

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