Question

the angle of elevation of a cloud from a point h metres above the lake is theta the angle of depression of its reflection in the lake is 45 degree then the height of cloud is​

Answer 1

Height of Cloud is $h(tan 45 + tan \phi)$m

Step-by-step explanation:

• Suppose A as Cloud Position & B be its Reflection's Position in Lake.

• Above 'h' meters above the lake is point E that makes Elevation Angle $\phi$ and Depression Angle 45° with B

• Height of Cloud = 'x'  

* Refer the attached figure for reference.

AC = BC = x,

DC = EF = h,

BD = x + h

AD = x - h

• Now, In ΔAED,  

$tan \phi = \frac {AD}{ED} = \frac {x - h}{ED}$ """(a)

• In Triangle EDB,

tan 45° = $\frac {DB}{ED} = \frac {x + h}{ED}$

• Hence, ED = (x + h)  """(b)

From (a) & (b) we get-

$\frac {x - h}{x + h} = tan \phi$

or $xtan \phi + htan \phi = x - h$

or $x(tan \phi - 1) = - h(tan \phi + 1)$

x = $x = \frac {h(tan \phi + 1)}{tan 45 - tan \phi}$

= $h(tan 45 + tan \phi)$

Finally, Height of Cloud = $h(tan 45 + tan \phi)$m

Answer 2

Step-by-step explanation:

here is the answer you are

looking

because tan(A+B)= tanA +tan B /1-tanA.tanB

so