Question

If the angles of elevation of a tower from two points distance a and b (a > b) from its foot on the same side of the tower have measure 30 and 60, then the height of the tower is ......,select a proper option (a), (b), (c) or (d) from given options so that the statement becomes correct.
(a) √a+b
(b) √ab
(c) √a-b
(d) √a/b

Answer 1

Dear student ,

Answer: Option b ( h = √ (ab) ) is correct.

Solution:

To find the height of tower, let it be h meters

now take a trigonometric ratio which includes both perpendicular and base

in Right angle triangle having 60° angle

tan 60 = h/b

√3 = h/b -------eq1

in Right angle triangle having 30° angle

tan 30 = h/a

1/√3 = h/a-------- eq2

multiply eq 1 and 2

√3 × 1/√3 = (h/b) × (h/a)

h²/ab =1

h² = ab

h =√(ab) meters

hope it helps you.

Answer 2

Height of the tower ( SR ) = h

Angle of elevation from two points

distance a and b from the foot

30° and 60° ,

<SPR = 30° ,

<SQR = 60° ,

PQ = a , QR = b ,

i ) In ∆PRS , <R = 90° ,

tan 30° = SR/PR

=> 1/√3 = h/a

=> a/√3 = h -------( 1 )

ii ) In ∆QRS , <R = 90°

tan 60° = SR/QR

=> √3 = h/b

=> √3 b = h ------( 2 )

Multiply ( 1 ) & ( 2 ) , we get

h × h = ( a/√3 )( √3 b )

=> h² = ab

h = √ab

Therefore ,
.
h = √ab

Option ( b ) is correct.

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