CBSE Class 10 Answered
At point A, 20m above the level of water in a lake angle of elevation of cloud is . The angle of depression of reflection of cloud in a lake at A is . Find the distance of cloud from A.
Asked by adalroshan2464 | 20 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
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 | 21 Aug, 2019, 10:28: AM
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