At point A, 20m above the level of water in a lake angle of elevation of cloud is 30 to the power of o. The angle of depression of reflection of cloud in a lake at A is 60 to the power of o. Find the distance of cloud from A.

Asked by adalroshan2464 | 20th Aug, 2019, 04:41: PM

Expert Answer:

 
AP is the height of point A from water lake.
let cloud is located at B and its reflection from water is located at C
let distance of cloud from point AD .e.g., DB = x
BQ = 20 + x
also QC = 20 + x
now, from ∆ADB,
tan30° = BD/AD 
1/√3 = x/AD 
AD = √3x ..............(1) 
from triangle ∆ADC, 
tan60° = DC/AD 
√3 = (x + 40)/√3x 
√3 × √3x = (x + 20 + 20) 
3x= x + 40
x = 20m.
hence, distance of cloud from A = 20m

Answered by Arun | 21st Aug, 2019, 10:28: AM