A vertical flagstaff stands on the top of a building. the hieght of the flagstaff above the building is 7m. the angles of elevation of the top and bottom of the flagstaff at a point on the level ground are 45 and 30 degree resp. Find the height of the building. (take root 3=1.73)
Answers
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.
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