Question

A vertical tower stands on a horizontal and is surmounted by a flagstaff of height 7m. from a point on the plane,the angle of elevation of the bottom of the flagstaff is 30° and that of the top of flagstaff is 45°.Find the height of the tower. Tell Fast​

Answer 1

Answer:

⇒ In △CBD,tan30

o

=

BC

BD

⇒

3

1

=

x

h

⇒ x=

3

h ----- ( 1 )

⇒ In△ABC,tan45

o

=

BC

AB

⇒ 1=

x

7+h

⇒ x=7+h

⇒

3

h=7+h [ From ( 1 ) ]

⇒

3

h−h=7

⇒ (

3

−1)h=7

⇒ h=

3

−1

7

⇒ h=

3

−1

7

×

3

+1

3

+1

∴ h=

3−1

7(

3

+1)

=

2

7(1.73+1)

=9.55m

∴ Height of the tower is 9.55m.

Step-by-step explanation:

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Answer 2

Let the height of tower be h

and the distance between the foot of tower to the point of sigh be x

[ previous solution is in the attachment ]

√3 ( 3h - h ) = 7√3

2h = 7√3/√3

2h = 7

h = 7/2

h = 3.5 m

Height of tower is 3.5m