if the angle of elevation of a cloud from a point ' h ' metres above a lake is alpha - Maths - Some Applications of Trigonometry

Question

if the angle of elevation of a cloud from a point ' h ' metres
above a lake is alpha and the angle of depression of its reflection
in the lake is beeta prove that the distance of the cloud from the
point of observation is 2h sec alpha
tan beeta - tan alpha??

Rahul Mishra · Accepted Answer

Let a be a point h metres above the pond AF and B be the
position of the Sky
We draw a line parallel to EF from A on BD at C

Clearly, BF = DF

Let, BC = m

so, BF = (m + h)

=> BF = DF = (m + h) metres

Now, in triangle BAC we have,

AB = m cosec α ---- (i)

and, AC = m cot α

Again,

in triangle ACD we have,
AC = (2h + m) cot β

so, m cot α = (2h + m) cot β

=> m = 2h cot β / (cot α - cot β)

putting, the value of m in (i) we get,

AB = cosec α [2h cot β / (cot α - cot β)] =
2h sec α / (tan β - tan α) proved !!

if the angle of elevation of a cloud from a point ' h ' metres above a lake is alpha and the angle of depression of its reflection in the lake is beeta. prove that the distance of the cloud from the point of observation is 2h sec alpha tan beeta - tan alpha??

if the angle of elevation of a cloud from a point ' h ' metres above a lake is alpha and the angle of depression of its reflection in the lake is beeta. prove that the distance of the cloud from the point of observation is 2h sec alpha

tan beeta - tan alpha??