from the top of a building 60m height the angle of prepration of the top and the botton of a tower are abserved to be 30° and 60° find the height of the tower
Answers
see required figure on attachment
Let AC be the tower and BE be the building. Let height of the tower be h m. It is given that the angles of depression of the top C and bottom A of the tower, observed from top of the building be 30° and 60° respectively. Hence, the height of the tower is 40 m.
Answer:
Let AC be the tower and BE be the building. Let height of the tower be h m. It is given that the angles of depression of the top C and bottom A of the tower, observed from top of the building be 30° and 60° respectively. Hence, the height of the tower is 40 m.
Step-by-step explanation:
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