Two buildings are at a distance of 15 root3 m from each other. A boy standing at the top of the smaller building is looking at the top and bottom of the other building. The angle of elevation and depression are 60º and 30° respectively. What will be the heights of the two buildings?
Answers & Comments
Step-by-step explanation:
Let the Height of the Tower be AD=h
and let the height of Building be CE=15
In △ADE
⇒tan60=
DE
AD
=
DE
h
⇒DE=
3
h
and we can see that BCDE is a Rectangle
⇒BC=DE=
3
h
and BD=CE
so, in △ABC
⇒tan30
o
=
BC
AB
=
h/
3
AB
⇒h=3AB⇒AB=
3
h
Now, it is given that CE=15⇒AD−AB=15⇒h−
3
h
=
3
2h
=15⇒h=22.5 m
and DE=
3
h
=
3
22.5
=13 m (Take
3
=1.73)