Correct option is (c) 11.55 m
Let CD is building A and B are two given points using horizontally on the same side of building.
In ΔDBC,
tan 60° = \(\frac{DC}{CB}\)
\(\sqrt 3 = \frac{10}y\) ......(1)
In ΔDCA,
tan 30° = \(\frac{DC}{CA}\)
\(\frac 1{\sqrt 3} = \frac{10}{x + y}\) .......(2)
From (1), put y = \(\frac{10}{\sqrt 3}\) in (2), we get
\(\frac 1{\sqrt 3} = \frac{10}{x + \frac{10}{\sqrt 3}}\)
\(\frac 1{\sqrt 3} = \frac{10\sqrt 3}{\sqrt 3x + 10}\)
\(30 = \sqrt 3x + 10\)
\(x = \frac{20}{\sqrt 3}\)
\(x = 11.55\) m
Hence, distance between two points A and B is 11.55 m.