Question

The 14th one pls I need it urgent!!

Answer 1

Answer:

The correct height of cloud =  h[(tanα + tanβ)]/(tanβ - tanα)  metre

Step-by-step explanation:

Here, let E be the point of observation such that ED = h metre

Let position of the cloud is A and the reflection of cloud in the lake is at F

Let AB = x

So, AC = CF

=>  AC = CF = x + h

Let angle of elevation of cloud ,α = ∠AEB

Let angle of depression of cloud , β = ∠BEF

Thus, in right ΔAEB

AB/BE = tanα

=> x/BE =  tanα

=> BE = x *  cotα            ------------------------(1)

Also, in right ΔBEF

BF/BE = tanβ

=> (CF + BC)/BE =  tanβ

=> (x + h + h)/BE =  tanβ

=> BE = (x + 2h) *  cotβ            ------------------------(2)

Comparing equations (1) and (2)

=>  x *  cotα =  (x + 2h) *  cotβ  

=> x * (cotα - cotβ ) = 2h * cotβ

=> x * (1/tanα - 1/tanβ) = 2h/tanβ

=>  x * (tanβ - tanα)/(tanα *tanβ)  = 2h/tanβ

=>  x = [(2h * tanα)]/(tanβ - tanα)

Thus, height of cloud = x + h

                                     = [(2h * tanα)]/(tanβ - tanα) + h

                                    = [(2h * tanα + h *tanβ - h *tanα)]/(tanβ - tanα)

                                    = [(h * tanα + h *tanβ)]/(tanβ - tanα)

                                    = h[(tanα + tanβ)]/(tanβ - tanα)  metre

Here, the angle β is more than angle α . So, in denominator (tanα - tanβ) is not possible as denominator becomes negative . So, in denominator value is  (tanβ - tanα) .

Thus, the correct height of cloud =  h[(tanα + tanβ)]/(tanβ - tanα)  metre