Question

$\large\mathbf{HEY\: QUESTION❤}$



The angles of depression of the top and bottom of a 12 m tall building, from the top of a multi-storeyed building are 30° and 60° respectively. Find the height of the multistoreyed building.

★ REQUIRED FULL EXPLANATION ANSWER​

Answer 1

Answer:

The height of the multi storey building and the distance between the two building is 43.704 m

Step-by-step explanation:

Refer the attached figure

Height of building i.e. AB = DC =8 m

The angle of depression to the top of the building AB from the top of a multi storey building i.e. ∠EAD = 30°

The angle of depression to the the bottom of the building AB from the top of a multi storey building i.e. ∠EBC = 45°

We are supposed to find the distance between two buildings i.e. BC =AD

Let ED be x

In ΔAED

Using trigonometric ratio

Tanθ=Perpendicular/Base

Tan30°=ED/AD

AD=X/1/√3 -1

In ΔEBC

Using trigonometric ratio

Tanθ=Perpendicular/Base

Tan45°=EC/DC

BC=8+xBC=8+x ---2

Since BC = AD

So, equate 1 and 2

8+x=x/1/√3

8+x=√3x

8=√3x-x

8=x(√3-1)

8=0.732050x

8/0.732050=x

10.92=x10.92=x

Substitute the value of x in 2

BC=10.92+32.784

BC=43.704

Hence the height of the multi storey building and the distance between the two building is 43.704 m.

Answer 2

The angles of depression of the top and bottom of a 12 m tall building, from the top of a multi-storeyed building are 30° and 60° respectively. Find the height of the multistoreyed building. ans. is in up