Question

The height of a house subtends a right angle at the window of another house situated just on the oposite side of the road.The angle of elevation of the top of the first house from the window is 30deg.If the road is 4sqrt3 meter broad,find hgt of 1st hous?

Answer 1

Let the height of first house be `AB=h` m
Width of the road `BR=4sqrt3` m
W is one window of second building where height `AB=h` forms
an angle `/_AWB=90^@` and the angle of elevation of top of the
first building `/_AWC=30^@`. So `/_CWB=60^@`

Now `(AC)/(CW)=tan30^@`

`=>AC=CWtan30^@=BRtan30^@`

Similarly

`(BC)/(CW)=tan60^@`

`=>BC=CWtan60^@=BRtan60^@`

Hence height of the first building

`h=AB=AC+BC=BR(tan30^@+tan60^@)`

`=4sqrt3(1/sqrt3+sqrt3)=(4+12)=16` m