Question

from the top of a building 60m high, the angles of depression of the top and bottom of a tower are observed to be 45° and 60° respectively. find the height of the tower and it's distance from the building
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Answer 1

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10th

Maths

Some Applications of Trigonometry

Heights and Distances

From thee top of a building...

MATHS

From thee top of a building 60m high the angle of depression of the top and the bottom of a tower are observed to be 30

o

and 60

o

. Find the height of the tower.

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ANSWER

in △ADE

tan60

o

=

DE

60

⇒DE=

3

60

=20

3

and we can see that , BCDE is a rec\tan gle

so, BC=DE⇒BC=20

3

and BD=CE.......(1)

and in △ABC

tan30

o

=

20

3

AB

⇒AB=20

3

×

3

1

=20

Now, as AD=AB+BD⇒60=20+BD⇒BD=40

and from (1)

BD=CE=40 (which is the height of the Building)

Therefore, Answer is 40

solution