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)

7.32 m

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