Question

the angle of depression of the top and bottom if an 8m tall building from the top of a multi storey building are 30°& 45° respectively. Find the height of the multi storey building and the distance between the two building?

Answer 1

it is the correct answer to this ❓

Answer 2

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

$Tan\theta = \frac{Perpendicular}{Base}$

$Tan30^{\circ} = \frac{ED}{AD}$

$AD= \frac{x}{\frac{1}{\sqrt{3}}}$ -1

In ΔEBC

Using trigonometric ratio

$Tan\theta = \frac{Perpendicular}{Base}$

$Tan45^{\circ} = \frac{EC}{BC}$

$BC=8+x$ ---2

Since BC = AD

So, equate 1 and 2

$8+x= \frac{x}{\frac{1}{\sqrt{3}}}$

$8+x= \sqrt{3}x$

$8= \sqrt{3}x-x$

$8=x (\sqrt{3}-1)$

$8=0.732050x$

$\frac{8}{0.732050}=x$

$10.92=x$

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.