Question

If the height of the building and distance from the building foot’s to a point is increased by 20%, then the angle of elevation on the top of the building: *​

Answer 1

Answer:

There will be no change in the angle of elevation.

Step-by-step explanation:

Let the height of the building be 'H'

and the distance between a point and the foot of the building be 'x'

Let the angle of elevation(∠ACB) be $\theta$₁

Refer to the attachment for the illustration.

Therefore, in Δ ABC

tan $\theta$₁  = H / x

Now as the height is increased by 20%

=> New height = Original height  + Increase

                        = H + (20/100) * H

                        = H + H/5

                        = 6H/5

Now as the distance between a point and the foot of the building is also increased by 20%

Let the angle of elevation(∠DEB) be $\theta$₂

Refer to the attachment for the illustration.

Therefore, in Δ DEB

=> New distance = Original distance  + Increase

                        = x + (20/100) * x

                        = x + x/5

                        = 6x/5

Therefore, angle of elevation = tan $\theta$₂= (6H/5)/(6x/5)

                                                             = H/x

which is the same as the original angle.

Therefore, there will be no change in the angle of elevation.

Answer 2

Answer:

There is no change in angle of elevation.

Step-by-step explanation:

In the context of the question;

We have to find the angle of elevation if the height of the building and distance from the building foot’s to a point is increased by 20%

Let the Initial height of the building be "H"

let the distance between a point and the foot of the building be 'x'

for initial condition ;

let the angle angle of elevation(∠ACB) be θ₁

as per the fig provided;

In Δ ABC;

tan θ₁ = H/x

Now as the height is increased by 20%

New height of the building  = Original height  + Increase

= H + (20/100) * H

= H + H/5

= 6H/5

Now as the distance between a point and the foot of the building is also increased by 20%

Let the angle of elevation(∠DEB) be θ₂

as per fig. provided

In Δ DEB

New distance = Original distance  + Increase

= x + (20/100) * x

= x + x/5

= 6x/5

New angle of elevation ;

tan θ₂ = (6H/5) / (6x/5)

tan θ₂ = H/x

as we can see,

tan θ₁ = tan θ₂

Therefore there is no change in angle of elevation