The angle of elevation of a cloud from a point 60m above the surface of water of a lake is 30° and the angle of depression of its shadow from the same point in the water of the lake is 60°.Find the height of the cloud from the surface of the water.
Answers
Answer:
120.
Step-by-step explanation:
let AB be the surface of the lake and P be the point of observation such that AP=60 meters. let C be the position of the cloud and C' be its reflection in the lake. then, CB=C'B. let PM be perpendicular from P on CB. then anglecpm=30degrees and angle C'pm = 60 degrees. let CM=h . then,CB=h+60. consequently,C'B=h+60.
tan30 degree=CM/PM.
=1/root 3=h/PM
PM=root3h..............(1)
in triangle PMC',we have
tan 60degree=C'M/PM
tan 60=C'B+BM/PM
root3=h+60+60/PM
PM=h+120/root3...........(2)
from equation (1) and (2),
root3h=h+120/root3
3h=h+120
2h=120
h=60....
now,CB=CM+MB= h+60 = 60+60 = 120...
hence,the height of the cloud from the surface of the lake is 120 meters...
hope it helps you mates..
Answer:
Let A be the cloud and D be its shadow.
BC = 60 m
Height of cloud = h m .
Total height of cloud = h + 60 m
In Δ ABE
h / x = tan 30
x = h √ 3
In Δ BDE
h + 60 + 60 / x = tan 60
h + 120 = x √ 3
2 h = 120
h = 60 m .
Therefore , height of cloud from surface of water = ( 60 + 60 ) = 120 m .
