Two windmills of height 50 CM and 40√3 m arein either side of the field. A person observes the top of the windmill from a point in between them. The angle of elevation was found to be 45° and 30°. Find the distance between the windmills .
with the picture representing the angle of elevation ,height
with the picture representing the angle of elevation ,height
Answers & Comments
Answer:
Read the problem carefully, convert the data into meaningful diagram.
Let AB be a tower of height =50 m
CD be another tower of height =40 m
The observe is at 'P' and angle of elevation ∠APB=∠CPD=45
o
Distance between BD=BP+PD
In △ABP,tanθ=
BP
AB
Therefore, tan45
o
=
BP
50
⇒1=
BP
50
.....(∵tan45
o
=1)
⇒BP=50 m
In △CPD,
tanθ=
PD
CD
⇒tan45
o
=
PD
40
....(∵tan45
o
=1)
⇒1=
PD
40
⇒PD=40 m
Thus BD=BP+PD=50+40=90 m
Therefore, the distance between the windmills on either side of field is 90 m.