Question

The angle of elevation of a patch of cloud from a point x meters and the above surface of pool is 30 degree and the angle of depression is 60degree what is the heght of cloud path above the surface of pool is

Answer 1

Step-by-step explanation:

triangle BEC  and BED are right angle triangles

in triangle BEC              tan30° = h-x/BE    ⇒BE = √3 (h-x) -------- (1)

in triangle BED    tan60° = h+x/BE ⇒   √3 BE = h+x ----------(2)  using first in second we get

√3(h-x) √3 = h+x     ⇒ h =2x

Answer 2

Given:

The angle of elevation from point 'x' m and above the surface of the pool = 30°

The angle of depression = 60°

To Find:

The height of the cloud path above the surface of the pool

Solution:

ΔBEC and ΔBED is a right-angled triangle..(i)

AB = 60m

C is the point of the cloud from the surface of the water.

Let CF be h meter.

From (i) ΔBEC and ΔBED are right angled triangles.

 EF = AB [both are 60m]

In ΔBEC,

tan B = $\frac{side opposite to angle B}{side adjacent to angle B}$

The value of tan30° is 1/√3.

tan30° = √3

tan30° = $\frac{CE}{BE}$

So, 1/√3 = $\frac{h-60}{BE}$

Now, BE = √3(h-60)m ..(ii)

In ΔBED,

The value of tan60° is √3.

tan B = $\frac{side opposite to angle B}{side adjacent to angle B}$

tan60° = $\frac{ED}{BE}$

∴ √3 = $\frac{h+60}{BE}$

So, √3BE = h + 60

Then, putting BE = √3(h - 60) from (ii)

    ⇒ √3 × √3(h - 60) = h+60

    ⇒ 3(h - 60) = h + 60

    ⇒ 3h - 180 = h +60

    ⇒ 3h - h= 60 + 180

    ⇒ 2h = 240

    ⇒ h = 240/2

    ⇒ h = 120m

Therefore, the height of the cloud path above the surface of the pool = 120m.