From a point P on the ground the angle of elevation of the top of 10 m high building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from the point P is 45°. Length of the flagstaff is:
(Take $\sqrt{3}$ = 1.732)
Answer & explanation
Correct answer: option 4
In triangle PBC ,
tan30º = \(\frac{ 1 }{ √3 }\) = \(\frac{ BC }{ PC }\)
\(\frac{ 1 }{ √3 }\) = \(\frac{ 10 }{ PC }\)
PC = 10√3
Now, In triangle PAC,
tan45º = \(\frac{ 1 }{ 1 }\) = \(\frac{ AC }{ PC }\)
\(\frac{ 1 }{ 10 √3}\) = \(\frac{ AC }{ PC }\)
AC = 10√3
AB = 10√3 - 10
= 10 ( 1.73 - 1 )
= 7.32
The correct answer is Option (4) → 7.32 m