Question

A 7m long flagstaff is fixed on top of a tower on the horizontal plane. from a point on the ground, the angle of elevation of the top and bottom of the flafstaff are 45degrees and 60degrees respectively. find the height of the tower

Answer 1

Hi ,

Draw a rough diagram according to

the problem ,


Let the distance from observer and foot of the tower = AB = x m

Height of the tower = BC = h m

Length of the flagstaff = CD = 7 m

Angle of elevation < DAB = 60 degrees

Angle of elevation = < CAB = 45

i ) from right angle triangle ABC,

< B = 90

Tan 45 = h / x

1 = h/ x

Therefore,
x = h ----------( 1 )

ii) from triangle ABD,

< B = 90

Tan 60 = ( 7 + h )/ x

Sqrt 3 = ( 7 + h )/ h from ( 1 )

Sqrt 3 × h = 7 + h

Sqrt3 × h - h = 7

h ( sqrt 3 - 1 ) = 7

h = 7 / ( sqrt 3 - 1 )

h = 7 × ( sqrt 3 + 1 )/( sqrt 3 -1)(sqrt3 +1 )

h = 7 ( sqrt 3 + 1 )/ [ ( sqrt 3 ) ^2 - 1 ]

h = 7 ( sqrt 3 + 1 )/ ( 3 - 1 )

h = 7 ( sqrt 3 + 1 )/2 m

Therefore ,
Height of the
tower( h )= 7( sqrt3 + 1 )/2m

I hope this will usful to you.

******