Question

A vertical flag staff stands on the top of a building the height of flagstaff above building is 6m the angle of elevation of the top and the bottom of the flag stuff at a point on the level ground are 45° and 30° respectively find the height of building

Answer 1

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Answer 2

Answer:

The height of the building is 8.19 m.

Step-by-step explanation:

Given : A vertical flag staff stands on the top of a building the height of flagstaff above building is 6 m the angle of elevation of the top and the bottom of the flag stuff at a point on the level ground are 45° and 30° respectively.

To find : The height of building?

Solution :

To determine the situation we create a rough image of the question,

Let the height of the building AC=h m

The height of the flagstaff is CD=6 m

Total height of the flag top from the ground AD=(6+h) m

The distance between the flag post and the point AB= x m

Refer the attached figure below.

ΔABC and ΔABD are right angle triangle formed,

In ΔABC and ΔABD, $\angle ABC=30^{\circ}$ and $\angle ABD=45^{\circ}$

Now, Applying trigonometric properties

In right angle triangle ΔABC,

$\tan 30^\circ =\frac{AC}{AB}$

$\frac{1}{\sqrt3} =\frac{h}{x}$

$x=h\sqrt3}$ .....(1)

In right angle triangle ΔABD,

$\tan 45^\circ =\frac{AD}{AB}$

$1=\frac{h+6}{x}$

$x=h+6$.....(2)

Equating the x from both equations,

$h\sqrt3=h+6$

$h\sqrt3-h=6$

$h(\sqrt3-1)=6$

$h=\frac{6}{\sqrt3-1}$

$h=\frac{6}{\sqrt3-1}\times \frac{\sqrt3+1}{\sqrt3+1}$

$h=\frac{6(\sqrt3+1)}{3-1}$

$h=\frac{6(\sqrt3+1)}{2}$

$h=3(\sqrt3+1)$

$h=8.19$

Therefore, The height of the building is 8.19 m.